This article focuses on the low-conservative stability criteria of delayed neural networks (DNNs). To achieve this goal, new techniques are developed to effectively utilize more system-related information. To use the time-varying delay information, some delay-product terms are introduced into the Lyapunov-Krasovskii functional (LKF), and an extended matrix-injection-based transformation method, which introduces delay-derivative-dependent slack matrices while obtaining the negative definite condition, is proposed. With respect to the use of activation function information, the terms related to the activation function are fully augmented in the LKF. In particular, by considering the sector-constraint information of the activation function, a new nonlinear-function-dependent functional term is established, and a sector-constraint-dependent matrix-separation-based inequality is developed. By applying the above techniques, several improved stability criteria are derived, and two typical examples are provided to illustrate the advantages of the proposed methods.

This article addresses the problem of resilient$H_\infty$control for direct-drive-wheel (DDW) systems by developing an adaptive hybrid-triggered (AHT) scheme that improves security and communication efficiency against hybrid cyberattacks. First, the attacked DDW system is modeled as a switched cyber-physical system (CPS) to effectively capture the impact of such attacks on signal transmission. Then, an attack-information-dependent AHT scheme is proposed, where triggering instants are determined by system states and attack information, and the adaptive threshold is tuned via a self-adaptive differential evolution (DE) algorithm to balance dynamic performance and communication frequency. By constructing a Lyapunov functional, sufficient conditions are derived to co-design the control gain and AHT parameters, ensuring global exponential stability and guaranteed$H_\infty$performance. Finally, the proposed method is validated on examples, showing its efficacy in maintaining system stability while considerably reducing communication overhead.

Load-frequency control (LFC) is commonly used in power systems to maintain the grid frequency. This article investigates the stability of LFC system containing time-varying delay with electric vehicles (EVs) and uncertain parameters. First, an improved model reconstruction technique is proposed to divide the state vectors of the system into$q$parts, where the first$q-1$parts are individual delay-state vectors and the$q{\text{th}}$part contains all other vectors. Unlike existing model reconstruction techniques that encapsulate all delay-state vectors into one part, the proposed method further reduces the dimensionality of the delay-state coefficient matrix. Second, based on the proposed model reconstruction technique, an augmented Lyapunov–Krasovskii functionals (LKF) is constructed in the form of additivity. This form reduces the number of decision variables, which greatly decreases computational complexity. Furthermore, in the derivative of LKF, the variable-augmented-based free-weighting-matrices technique is introduced only for time-delay state vectors, further reduces the conservatism with an acceptable computational complexity. Finally, two numerical examples are used and RT-LAB simulation experiment is conducted to verify that the proposed stability criterion can achieve high accuracy while reducing computational complexity significantly. Meanwhile, the effect of system parameters on delay margins is also discussed.

This article investigates the practical fixed-time synchronization (FxTS) for complex dynamical networks (CDNs). Given the notable benefits associated with intermittent control, wherein control inputs are activated solely during the working phase of each control cycle, and event-triggered control, which significantly curtails the frequency of control input updates, this article proposes an intermittent event-triggered control scheme aimed at achieving practical FxTS in CDNs. The proposed scheme substantially mitigates the volume of information transmitted across the network while concurrently reducing control-related expenditures. To mitigate the issue of high-frequency buffeting, the newly devised control scheme employs a saturation function as a substitute for the conventional signum function. Subsequently, this article presents a more precise estimation approach for reasonably approximating the synchronization time (ST) of CDNs and the synchronization error (SE) induced by the integration of the saturation function. Moreover, this article imposes constraints on the frequency and total duration of communication pauses in an average-sense manner and constructs a piecewise Lyapunov function to further deduce several less conservative criteria for practical FxTS. Finally, two illustrative examples are provided to demonstrate the viability of the intermittent event-triggered control scheme and the accuracy of the ST and SE estimations.

This study addresses the resilient control of connected and automated vehicle (CAV) platoons under denial of service (DoS) attacks. We investigate two main attack scenarios. In the first scenario, zero-input DoS attacks target the communication channels, and progressing from degraded vehicle communication ability to compromised leader reachability may cause complete platoon disconnection. The second scenario considers the simultaneous occurrence of the above zero- and hold-input DoS attacks, where the latter introduces control delay. With Lyapunov functions and dwell time methods, switching distributed controllers are developed to achieve input-to-state string stability (ISSS). This ensures robust platoon performance through spacing regulation, speed consensus, and state error attenuation along the platoon, even under different attack conditions. Numerical simulations demonstrate the platoon’s resilience against simultaneous zero-input and hold-input DoS attacks, highlighting their cascading effects on platoon performance.

The issue of stability analysis of delayed neural networks (DNNs) is investigated in this study. To begin with, a Lyapunov-Krasovskii functional (LKF) with adjustable delay intervals is proposed to consider more delay information, in which an adjustable parameter is introduced to divide the delay interval to get optimal stability analysis results. Then, by combining with the delay-interval-adjustable-based idea, the delay interval of the single integral term in the LKF derivative is divided into three parts. Meanwhile, a more general condition related to the neuron activity function and the divided delay intervals is constructed to contain more neuron activity function and delay information. Lastly, an improved stability analysis criterion of DNNs is obtained, which is validated through a numerical example.

This paper investigates the stability analysis of the delayed T-S fuzzy systems with less conservatism by exploring the monotone increasing or decreasing characteristics of periodically varying delay. Firstly, we introduce a novel delay-set-partitioning-based (DSPB) approach via combining the allowable delay sets (ADS) method with the region partitioning methodology. Then, an improved DSPB Lyapunov–Krasovskii functional (LKF) together with DSPB FWMs method is proposed building upon this framework. Compared with the existing methods, the proposed methods tailor the construction of the LKF and FWM to each sub-ADS, thereby enhancing flexibility and reducing conservatism in stability analysis. As a result, we derive less conservative stability criteria for delayed fuzzy systems. Finally, the superiority and improvement of the proposed methods are validated through an illustrative numerical example.

This study proposes a multi-rate sampled-data control framework for quarter-vehicle active suspension systems (QVASSs), where asynchronous sensor sampling mechanisms are systematically modeled via the input delay approach. Firstly, during the modeling of the QVASS, different system states are considered to be acquired by three distinct sensors and transmitted through independent control loops. Secondly, leveraging the input delay approach, the result of the H∞performance analysis is given by proposing a Lyapunov-Krasovskii functional incorporating multi-rate state information. Subsequently, congruence transformations are employed to derive the H∞controller design criterion under hardware constraints. Finally, experimental validation demonstrates the advantage of the proposed method: the multi-rate sampled-data controller exhibits design flexibility and superior control performance compared to conventional approaches.

This paper is concerned with the stability analysis of Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. First, by constructing a generalized line-integral Lyapunov function (GLILF), applying the free-matrix-based inequality and the delay-derivative-dependent free-weighting-matrices method, a basic stability criterion is derived. Besides, the structure of the matrices in the stability criterion is reconstructed through congruent transformation, and an improved stability criterion is derived accordingly. To clarify the advancement of the proposed method, a stability condition is given without the GLILF. Finally, two numerical examples and a practical example are applied to show the advancement and merits of the presented method.

This paper presents a novel time-varying formation (TVF)$H_{\infty }$tracking controller for multi-agent systems (MASs) under exogenous disturbances and time-varying delays. In order to address the issue that most of the existing formation controllers are designed under the predetermined small time delay, a formation controller which can tolerate a large delay upper bound is designed. This is achieved by employing the Lyapunov functional method. At the same time, in order to suppress the influence of exogenous disturbances on the formation process, the robustness of the formation controller is improved through optimizing the$H_{\infty }$performance index. To derive the gain matrix of the formation protocol, a mere two linear matrix inequalities (LMIs) need to be resolved. On this basis, differential evolution (DE) algorithm is employed to further adjust and optimize the parameters of the formation controller. Finally, it is proved that the obtained results can be directly applied to resolving the leader-follower consensus problem. Two simulation experiments are carried out to verify the superiority and effectiveness of the proposed scheme, where four followers achieve the$H_{\infty }$formation tracking following the leader. Note to Practitioners—The motivation of this article is to address the TVF$H_{\infty }$tracking control problem for MAS under limited network communication resources. The TVF model is extensively applied in the flocking control domain, such as robot formation control, spacecrafts formation flight and so on. In the engineering application scenarios, the communication between agents usually has the following problems: 1) The information interaction among the agents is often influenced by exogenous disturbances and time delays; 2) The existing formation tracking controllers are only suitable for handling predetermined small time delay. Thus, this paper presents a TVF$H_{\infty }$tracking controller with excellent robustness to deal with these problems, and this controller is optimized based on a DE algorithm.

In this article, the time-varying formation-containment control problem of heterogeneous multi-agent systems (MASs) with an observer-based state feedback protocol is studied, where both communication delays and output delays are taken into consideration. By introducing an augmented Lyapunov-Krasovskii functionals (LKFs) candidate and employing less conservative methods to estimate its derivative, an improved quasi-formation-containment criterion is derived. On this basis, some observers and controllers are designed to allow for a larger maximum upper bound (MUB) of time delays on the premise of guaranteeing the fulfillment of the time-varying formation of leaders and the bounded convergence of followers. The estimation of the MUB determines the allowable delay range for system stability under the designed observers and controllers. Moreover, a distributed algorithm is developed to calculate the MUB of time delays, the observer gains, and the controller gains. Finally, two simulation experiments are implemented to demonstrate the obtained results, which verify the superiority and practicability of the criterion and algorithm.

Modern power systems maintain frequency stability through load frequency control (LFC), which is affected by delays of control signals and the volatility of renewable energy sources. This paper investigates the robust problem of LFC for wind power systems with multi-source-induced delays, considering the significant variations in delay magnitudes across different time intervals due to diverse inducing sources. Firstly, the LFC is modeled as a closed-loop system with two switching modes by dividing the delay into two parts with different magnitudes based on the inducing sources. Then, the controller design criteria for a multi-source-induced delay-dependent LFC system are proposed through the switching system theory. Finally, case studies conducted on two-area and three-area LFC system validate that the method proposed in this paper can enhance the robust performance of the system compared to general methods, and it is also capable of handling certain multi-source-induced delay phenomena that are beyond the capabilities of general methods during the operation of LFC systems. Note to Practitioners—Frequency stability in multi-area power systems is facing growing challenges due to delays caused by various sources. Existing methods for delayed power systems often overlook these diverse delay sources, treating them as uniform, which may reduce system robustness. This paper proposes a robust load frequency control (LFC) scheme based on a delay-induced-source dependent approach, which aims to ensure the exponential stability of multi-area LFC systems. By modeling multi-source-induced delays using switching modes and designing controllers through switching system theory, this method effectively addresses the complexity of multi-source-induced delays. Furthermore, it enables the design of controllers tailored to the type of delay-inducing source, enhancing system stability under different delay types. Practitioners can apply this method to enhance the reliability of LFC systems in power systems experiencing diverse delay scenarios. It is especially effective in situations where existing methods struggle to handle complex delays, providing a practical solution for maintaining frequency stability in modern networked power systems.

The resilient control design for wireless networked control systems (WNCSs) under Denial-of-Service (DoS) attacks is investigated based on the sampled-data theory in this study. Firstly, by employing a logic processor module in the control center, WNCSs under DoS attacks are modeled as aperiodic sampled-data systems (SDSs). This integrates the duration of DoS attacks into the sampling intervals, simplifying the controller design without the need for additional handling of DoS attacks. Then, a sawtooth-characteristic-based hierarchical integral inequality is presented to leverage the underused sampling sawtooth characteristic in existing studies in WNCSs under DoS attacks. Next, a high-order two-sided looped-functional caters for the proposed hierarchical integral inequality is constructed and the sawtooth-dependent free-weighting matrices are introduced into the constraint of system equation to further preserve the information of SDSs. These improvements of methodological promote a reduction in the conservatism of the stability criteria. Consequently, a resilient controller design scheme is presented based on the system substitution-based de-coupling method, resulting in a controller that exhibits enhanced counteraction against DoS attacks. The efficacy of this controller design scheme is demonstrated through a satellite control system and a load frequency control power system, showcasing the advantages of the resilient controller. Note to Practitioners—This research offers significant insights into enhancing the resilience of WNCSs against DoS attacks, which is a prevalent challenge in industrial network security. The developed solution is particularly beneficial in industries where maintaining uninterrupted control communications is critical, such as satellite systems and power systems that are vulnerable to malicious DoS attacks. The logic processor module provides a practical approach to dynamically monitor the strength and duration of DoS attacks. Based on this, the relevant system is re-modeled as an aperiodic SDS. This integration with the existing sampling theories ensures that the system makes good use of current technologies and facilitates the design of resilient controllers that can withstand DoS attacks. On the one hand, the application of this enhanced control design allows for a more robust system that maintains functionality under cyber attack conditions, thereby protecting critical operations and potentially reducing downtime and associated costs. On the other hand, this approach reduces the conservatism of controller design guidelines, allows for more efficient utilization of network resources, and improves system response. However, this approach relies heavily on the accuracy and timeliness of the logic processor’s response to DoS attacks. This may not be entirely reliable in environments with highly irregular or complex network threats.

This paper presents an adaptive dynamic surface control (DSC) method for nonlinear systems with multiple disturbances, parameter uncertainties, and unknown nonlinear dynamics, using a reduced-order extended state observer (ROESO). Compared to related methods, this proposed approach offers several distinct advantages: (i) The method does not require knowledge of the upper bound function for unknown nonlinear dynamics, allowing the controlled plant to not be bounded-input bounded-state, thus expanding the applicability of the DSC method; (ii) By utilizing known model information, an ROESO is designed to handle mismatched uncertainties and disturbances, reducing the load on the observer and enhancing its capability to suppress unknown nonlinear dynamics; (iii) This method employs an adaptive output-feedback DSC approach, which is more practical and easier to implement than state-feedback methods; and (iv) The observer gain, adaptive gain, and DSC gain are simultaneously optimized using a particle swarm optimization algorithm. Additionally, detailed stability analysis is provided, and simulations and comparative experiments are conducted on a rotational system to demonstrate the efficacy and superiority of the proposed method. Note to Practitioners—Most real systems are nonlinear and subject to a variety of matched and unmatched uncertainties and disturbances. Adaptive control is an effective method for dealing with parametric uncertainty, but requires that the uncertainty can be represented linearly in terms of unknown parameters and cannot handle exogenous disturbances. As an alternative active disturbance attenuation method, disturbance/uncertainty estimation and attenuation techniques have a two-degree-of-freedom control structure. However, for nonlinear systems, they simply estimate and compensate for the nonlinear characteristics of the system as disturbances, which, although effective, can lead to problems such as excessive inputs in the actual control, thus affecting the performance of the system. Backstepping control is one of the most powerful tools for handling nonlinear systems to deal with mismatched disturbances and has been well used in various fields, but it usually suffers from the problem of “explosion of complexity”. Thus, how to deal with various matched and unmatched uncertainties and disturbances in a nonlinear system is still a challenge. Motivated by these considerations, this paper presents an adaptive output-feedback dynamic surface control method for a class of uncertain nonlinear systems with multiple mismatched uncertainties and disturbances.

This paper uses a proportional-integral (PI) controller to achieve the exponential synchronization of chaotic Lur’e systems under aperiodic sampled-data control. First of all, in order to achieve synchronization of the chaotic Lur’e systems, an aperiodic sampled-data PI controller is constructed. The controller in question incorporates a greater amount of information derived from the sampling sequence than the sampled-data proportional controller. Subsequently, a virtual variable is introduced based on an intermediate variable, thereby constructing a dimension-enhanced synchronization error system. A novel criterion is developed based on virtual variable-related equations for the design of sampled-data PI controllers, with the objective of achieving larger sampling periods and exponential convergence rates in the synchronization process. In the next, a numerical example of neural networks is presented, demonstrating how the developed method in this paper enhances the dynamic performance of the synchronization process in comparison to existing methods. Finally, the developed method is applied to Chua’s circuits, where the real-circuit experiment is made to show its effectiveness.

The issue of extended dissipativity analysis (EDA) for delayed Markovian jump neural networks (MJNNs) is investigated in this article. First, a delay-interval-adjustable-based Lyapunov-Krasovskii functional (LKF) is proposed, in which the delay interval is adjusted by a tunable parameter to obtain an optimal extended dissipativity result, offering a new idea to enhance the consideration of delay information. Furthermore, to take into account more effective information, the LKF is augmented with both single and quadratic integral variables. Accordingly, the LKF derivative becomes a higher-order term of the time-varying delay. To solve this nonlinear problem, a variable-augmented-based free-weighting-matrices approach is employed to transform the nonlinear term into a linear form and provides more freedom in obtaining enhanced EDA results. Then, two novel extended dissipativity criteria of delayed MJNNs are derived. Meanwhile, to show the general applicability of the proposed methods, the derived criteria are applied to the EDA and stability analysis for delayed neural networks (NNs). Lastly, the merits and effectiveness of the proposed techniques are demonstrated through three numerical examples and a real-world application of a quadruple-tank process system. Additionally, the proposed methods can be effectively applied to the practical fields of power system stability control, robot motion control, and image processing, while reducing the conservatism of system performance results.

In this work, membership-functions-dependent resilient hybrid-triggered (HT) passivity control is considered for networked fuzzy systems against deception attacks. To mitigate the transmission burden and enhance resilience to attacks, a resilient membership-functions-dependent HT mechanism is proposed that considers the properties of a Takagi-Sugeno fuzzy model. The presented HT strategy incorporates membership functions to generalize the HT threshold and weighting matrices. Then, the membership functions are embedded in quadratic and integral terms of the fuzzy Lyapunov-Krasovskii functional, leading to a more effective resilient HT mechanism that significantly reduces network bandwidth stresses and achieves better passivity performance. An asynchronous passivity fuzzy controller with enhanced feasibility is designed under imperfect premise matching, and traditional passive controllers are generalized as special cases. Finally, a truck-trailer example is offered to test the validity and applicability of the proposed techniques.

This article investigates the $H_{\infty }$ -based tracking control problem for nonlinear systems through the Takagi-Sugeno (T-S) fuzzy technique. A nonuniform sampled-time-dependent functional (NSTDF) is proposed, which removes the constraints of the conventional looped functional (LF) and relaxes the condition of the functional derivative. Combining the NSTDF with $H_{\infty }$ theory, a novel theorem for $H_{\infty }$ performance analysis of sampled-data systems is given, which loosens the positive-definite constraint on Lyapunov matrices in traditional LFs. By introducing the error integral state, an augmented system is constructed, and a proportional-integral (PI)-type controller that incorporates the external disturbance, transmission delay, and packet dropouts is designed to enable the tracking control. Thus, the $H_{\infty }$ -based tracking control issue is converted into an $H_{\infty }$ -based control problem for the augmented system, and the control conditions are derived via the proposed methods. Finally, the wind energy conversion system (WECS) and Rossler's system clarify the feasibility and merits of the provided methods.

This article develops a novel robust control methodology for nonlinear multiagent systems (MASs) to address the time-varying formation (TVF) problem. The methodology offers a concise yet efficacious technique based on the Lyapunov functional for more general one-sided Lipschitz (OSL) nonlinear MASs with external disturbances and time-varying delays. Note that most existing TVF controllers can only achieve formation targets under small delays, which significantly limits their performance. The proposed TVF control method in this article demonstrates remarkable robustness by effectively accommodating larger delays and additionally mitigating the impact of disturbances on MASs. On this basis, a robust TVF controller optimization scheme of MASs combined with the particle swarm optimization (PSO) algorithm is proposed. Comparing the optimized results with those under conventional control methods, it has been proved that optimized controller has obvious improvement on the formation performance of MASs. Finally, the feasibility and the superiority of the developed TVF control approach are validated by a simulation of an autonomous aerial vehicle swarm system (AAVSS) composed of six AAVs.

The frequency stability of multiarea power systems is guaranteed by networked load frequency control (LFC). Time delays due to occasional congestions/attacks in the LFC are often much longer than those from signal transmissions during normal communication, which invalidates the previous stability assessment methods. In this article, a novel stability analysis method for this scenario via a segmented delay description and a switched system is proposed. First, a two-piecewise function is used to describe multisource-induced delays, including large delays under occasional harsh network conditions and small delays under smooth network conditions; thus, a multiarea LFC model with multisource-induced delay is established. The stability criteria, which is based on switched system theory, reveals the relationship between delay characteristics and system stability. Finally, the proposed method is used to assess the delay tolerance of the LFC in traditional/deregulated environments. The results show that even with a large delay causing instability, as long as it meets certain frequency and duration constraints, the LFC remains stable. This novel discovery reflects the essential improvements of the proposed method and is useful for designing better control strategies.

This article investigates observer-based optimal fuzzy control for networked interval type-2 (IT-2) fuzzy systems against hybrid cyber-attacks, including aperiodic denial-of-service and deception attacks. First, a hybrid cyber-attack model is constructed after denoting a nonlinear system with parameter uncertainties and external disturbances via an IT-2 fuzzy model. Then, the switched fuzzy observer is derived to estimate the unmeasured states of the system. Second, by introducing the newly designed algorithm, a novel optimal adaptive fuzzy event-triggered strategy is proposed. This mechanism effectively reduces the communication burden and enhances flexibility in handling hybrid cyber-attacks. Third, by employing a new piecewise Lyapunov–Krasovskii functional that incorporates membership functions (MFs), a fuzzy controller with imperfect MFs is designed, where both the MFs and their derivatives are considered. Eventually, sufficient conditions are developed to ensure that the networked IT-2 system is mean square exponentially stable with$ H_\infty$performance. Finally, the merits and applicability of the proposed approaches are exemplified by a practical example.

This paper focuses on the stability analysis and stabilization design of Takagi-Sugeno (T-S) fuzzy systems under sampled-data control. Firstly, by capturing the constant characteristic of the sampling time in the sampling interval, a novel sampling-fuzzy-dependent LyapunovCKrasovskii functional (LKF) is proposed, which can introduce both fuzzy-dependent and sampling-dependent information and avoid the derivatives of membership functions (MFs). Secondly, a novel synchronization method via the slack membership-dependent matrices is proposed to synchronize the mismatched MFs between the plant and controller, which can overcome the limitations that the membership functions must be greater than zero in existing works. Thus, improved stability and stabilization conditions are obtained. Finally, two case studies are given to show the effectiveness and merits of the proposed methods.

This paper is dedicated to addressing the event-triggered$H_{\infty }$control problem for interval type-2 fuzzy systems. A weakly constrained event-triggered functional is proposed by incorporating the event-triggering variable and$H_{\infty }$performance index, which relaxes the restrictions imposed on Lyapunov functionals in existing sampled-data control studies. This functional also provides a graceful event-triggered$H_{\infty }$analysis framework that avoids the use of the$S$-procedure. Then, the Lyapunov matrices in the functional are set to be aperiodic sampling-dependent, thereby further reducing the conservatism of the criteria. Furthermore, a basic-inequality-based method is provided to handle the imperfect premise matching between the fuzzy system and the fuzzy controller in interval type-2 fuzzy systems, avoiding the previous introduction of additional free matrices and extra constraints. Thereafter, the fuzzy controller design method is given, and the aperiodic sampling-based static/dynamic event-triggered control is effectively implemented. Ultimately, two case studies validate the effectiveness of the proposed approaches and demonstrate their ability to achieve superior event-triggered control effects compared with the existing literature.

This paper addresses the stability and stabilization issues of Takagi-Sugeno (T-S) fuzzy systems under sampled-data control. In this paper, efforts are dedicated to developing a stability criterion and control strategy with high accuracy and low complexity, leveraging an improved looped functional and a fuzzy-related matrix injection method. First, an improved looped function containing quadratic information about the sampling sawtooth characteristic is employed to include as much system state information as possible in a simple form. In response to the nonlinear terms encountered in the functional derivatives, a fuzzy-related matrix injection method is proposed on the basis of linearization transformation. This method enables the unified treatment of reciprocally convex and quadratic terms, which is conducive to reducing estimation gaps. Based on the aforementioned techniques, stability and stabilization criteria for T-S fuzzy systems are derived. The efficacy and superiority of the proposed method are substantiated through rigorous theoretical analysis and illustrative instances.

Smart grids usually apply digital load frequency controller to regulate the frequency via the wide-area communication network, where the data sampling and transmission delay of the signal transmission may degrade the frequency control performance. Plus, the inherent nonlinearity of frequency regulate may weaken the control performance. In this paper, a digital PID-type load frequency control (LFC) scheme based on warm up gray wolf optimization algorithm is designed for large-scale renewable energy grid-connected smart grids, considering the influence of data sampling, transmission delay and nonlinearity. First, a new digital PID-type LFC model considering data sampling, transmission delay and nonlinearity is established. Second, a novel warm-up gray wolf optimization method is proposed to optimize the parameters of the digital PID controller. The method can fully consider the nonlinearity of LFC and the influence of time delay and sampling, and the PID parameters with optimal control performance can be derived by taking the control performance as the objective function. Finally, simulation tests are undertaken on the three areas LFC systems. The simulation results illustrate the effectiveness and superiority of the proposed LFC scheme, and the necessity of control scheme design to consider the data sampling, transmission delay and nonlinearity.

The storage sources in auxiliary frequency regulation service (AFRS) for load frequency control (LFC) have a fast response time and are effective in smoothing wind power output. In this article, the disturbance suppression ability for delayed LFC is evaluated considering the participation of electric vehicle (EV) aggregators and redox flow batteries (RFBs)-based AFRS. First, a model for the delayed LFC with wind power is constructed, incorporating the EV aggregator and RFB participation. A criterion for evaluating the disturbance suppression ability of delayed LFC is presented, incorporating more system information to reduce conservativeness compared to existing methods. Finally, case studies show that the introduction of RFBs improves the disturbance suppression ability and the delay tolerance ability of LFC. Simulation and experimental tests demonstrate that the theoretical improvement produces more accurate evaluation results.

The time delay, disturbances, and parameters uncertainties brought by open communication networks and renewable energy source threaten the stable operation of the frequency control system (FCS) in microgrids (MGs). Plus, the low inertia of MGs exacerbates frequency fluctuations. In this article, the codesign of$ H_{\infty }$robust controllers for secondary frequency control (SFC) and virtual inertia control (VIC) in the delay-dependent FCS of MG is presented. First, the FCS of MG considering the VIC under the influence of the time delay is established. Second, based on Lyapunov stability theory, an$ H_{\infty }$performance analysis method is proposed for the FCS of MG with the time-varying delay. Then, with robust performance index as the design condition, the grey wolf optimizer is used to carry out the codesign of the SFC and VIC. Finally, the simulation test proves that the proposed control strategy can effectively codesign the SFC and VIC. The designed robust controllers can effectively deal with the problems of low inertia, time delay, disturbance, and parameters uncertainty in MG frequency control.

Recent studies have identified microvascular invasion (MVI) as the most vital independent biomarker associated with early tumor recurrence. With advancements in medical technology, several computational methods have been developed to predict preoperative MVI using diverse medical images. These existing methods rely on human experience, attribute selection or clinical trial testing, which is often time-consuming and labor-intensive. Leveraging the advantages of deep learning, this study presents a novel end-to-end algorithm for predicting MVI prior to surgery. We devised a series of data preprocessing strategies to fully extract multi-view features from the data while preserving peritumoral information. Notably, a new multi-branch deep fused feature algorithm based on ResNet (DFFResNet) is introduced, which combines Magnetic Resonance Images (MRI) from different sequences to enhance information complementarity and integration. We conducted prediction experiments on a dataset from the Radiology Department of the First Hospital of Lanzhou University, comprising 117 individuals and seven MRI sequences. The model was trained on 80% of the data using 10-fold cross-validation, and the remaining 20% were used for testing. This evaluation was processed in two cases: CROI, containing samples with a complete region of interest (ROI), and PROI, containing samples with a partial ROI region. The robustness results from repeated experiments at both image and patient levels demonstrate the superior performance and improved generalization of the proposed method compared to alternative models. Our approach yields highly competitive prediction results even when the ROI region outline is incomplete, offering a novel and effective multi-sequence fused strategy for predicting preoperative MVI.

In this article, an optimal surrounding control algorithm is proposed for multiple unmanned surface vessels (USVs), in which actor-critic reinforcement learning (RL) is utilized to optimize the merging process. Specifically, the multiple-USV optimal surrounding control problem is first transformed into the Hamilton-Jacobi-Bellman (HJB) equation, which is difficult to solve due to its nonlinearity. An adaptive actor-critic RL control paradigm is then proposed to obtain the optimal surround strategy, wherein the Bellman residual error is utilized to construct the network update laws. Particularly, a virtual controller representing intermediate transitions and an actual controller operating on a dynamics model are employed as surrounding control solutions for second-order USVs; thus, optimal surrounding control of the USVs is guaranteed. In addition, the stability of the proposed controller is analyzed by means of Lyapunov theory functions. Finally, numerical simulation results demonstrate that the proposed actor-critic RL-based surrounding controller can achieve the surrounding objective while optimizing the evolution process and obtains 9.76% and 20.85% reduction in trajectory length and energy consumption compared with the existing controller.

This article studies the stability and stabilization of delayed Takagi–Sugeno fuzzy systems (TSFSs). First, by introducing the membership functions into the free matrices, a membership-dependent (MD) Free-weighting-matrices (FWMs) method containing the variable-augmented-based FWMs method is proposed. This method can avoid the time-varying delay-dependent higher-order terms in the derivatives of the Lyapunov-Krasovskii functionals and introduce MD information. Then, an improved stability criterion is derived by applying the MD FWMs approach with the generalized free-matrix-based inequality. Moreover, through the parallel distributed compensation technology, a related controller design approach for the closed loop TSFS is developed. Finally, four known numerical examples are shown to validate the improvements and advancements of the presented method.

This article addresses the consensus control and optimization issue for multiagent systems (MASs) with time-varying delay. Different from existing ones, an order-reduction method (ORM) is proposed to reduce the order of linear matrix inequalities (LMIs) without a complicated calculation process. The problem of complexity explosion caused by using LMI to analyze MASs is solved. To start with, we discuss and compare the existing ORMs and our ORM, respectively. Subsequently, under this improved ORM and the quadratic-delay-product method, a modified Lyapunov-Krasovskii functional (LKF) is constructed to obtain a less conservative consensus criterion. Then, we put forward a consensus controller which allows larger time delay upper bound. In addition, based on the self-adaptive differential evolution (DE) algorithm, the performance of the controller is significantly optimized. It is strictly proved that the designed controller can guarantee the realization of consensus and the LMI method used is feasible because it is independent of the number of agents. Finally, the simulation and comparison results illustrate the superiority of the theoretical results over others.

The stability issues of linear systems with time-varying delays are tackled in this article. Several positive augmented Lyapunov-Krasovskii (L-K) functionals are proposed by introducing integral quadratic functions based on the L-K stability theorem. To further reduce the estimation gap caused by the existing integral inequalities, which were applied for dealing with the derived augmented-type integral term from augmented functional, some refined matrix-separation-based inequalities are introduced. With fewer decision variables, the proposed method considers the information among the system state, its derivative, and their related terms. After these, some cubic functions in the time-varying delay appear and show nonconvexity. Then, negative definite conditions are imposed on such cubic terms to obtain the stability criterion in the form of the linear matrix inequality (LMI). Inspired by the Taylor’s expansion methodology and the delay-partitioning techniques, we improve the existing negative definite conditions on the cubic function without introducing any decision variable. For linear systems with a time-varying delay, this relaxed condition, the refined matrix-separation-based inequalities, and the constructed L-K functionals, are combined to produce a less conservatism stability criterion. Two numerical examples illustrate the effect of the offered methods and the stability condition.

This article studies nonconservative stability conditions of continuous-time switched linear systems under mode-dependent dwell time (MDT). To establish a unified analysis approach for switched systems with stable and/or unstable subsystems, a concept called “dictionary” is introduced to characterize admissible MDT switching sequences. Subsequently, two equivalent nonconservative conditions of the global uniform asymptotic stability (GUAS) are obtained based on quadratic Lyapunov functions (LFs). Moreover, the stability results are transformed into convex conditions for facilitating the controller design. In addition, the developed stability results are applied toL2-gain analysis andH∞controller design for the continuous-time switched linear system subject to external disturbances. Simulations are provided to validate the effectiveness and the superiority over existing results.

In this paper, the time-varying formation tracking (TVFT) problem of multi-leader multi-agent systems (MASs) under sampled-data control is studied. First, an improved TVFT criterion is derived by employing a general looped-functional and a zero integral functional. Then a new TVFT controller is designed based on our proposed method. Unlike the existing works, the TVFT controller can allow for bigger sampling intervals of multi-leader MASs. The results demonstrate that the states of the followers can form the designated formation and rotate around the convex combination formed by the multiple leaders. In addition, we generalize the results of TVFT to the sampled-data consensus for MASs, a sampled-data consensus controller which can reduce communication consumption is designed. Meanwhile, the values of the allowable maximum sampling intervals (AMSIs) are calculated. Finally, the superiority and availability of the theoretical results are verified by two simulation experiments.Note to Practitioners—The motivation of this paper is to address the problem of TVFT for MAS with multiple leaders. It has been applied to several practical engineering systems, e.g., satellite formation control and unmanned air vehicles (UAVs) formation control. Note that information exchange is a prerequisite to ensure safe and stable control of multi-UAV formation. However, continuous-time communication is difficult to be realized in the actual environment, and it will inevitably consume a lot of energy. In addition, sampled-data controller for MAS with a small sampling interval may cause network congestion. Therefore, a sampled-data controller which allows for a bigger sampling interval for MAS is designed to save network resources in this paper. Through simulation experiments, it can be proved that the followers not only track the leaders, but also form the designated formation.

This article investigates the consensus problem of multiagent systems (MASs) with time-varying delays subject to switching topologies. For the purpose of obtaining less conservative consensus conditions, first, a delay-product-type Lyapunov-Krasovskii functional (LKF) based on the auxiliary function-based integral inequality (AFBII) is constructed. Then, the generalized reciprocally convex matrix inequality (GRCMI) and a relaxed quadratic function negative-determination lemma are introduced to obtain the maximal-allowable upper bound of time-varying delays. Moreover, a proportional and derivative-like (PD-like) protocol is designed and the result is extended to the leader-following consensus of agents under Lipschitz nonlinear dynamics. Finally, two illustrative examples, including Chua's circuit, are given to demonstrate the advantages of the new consensus criteria.

This research investigates the stability of discrete-time neural networks (DNNs) with a time-varying delay by using the Lyapunov-Krasovskii functional (LKF) method. Recent researches acquired some less conservatism stability criteria for time-varying delayed systems via some augmented LKFs. However, the forward difference of such LKFs resulted in high-degree time-varying delay-dependent polynomials. This research aims to develop some augmented state-related vectors and the corresponding extended free-weighting matrices zero equations to avoid the appearance of such high-degree polynomials and help to provide more freedom for the estimation results. Besides, an augmented delay-product-type LKF is also established for ameliorating the stability conditions of the time-varying delayed DNNs. Then, based on the above methods and Jensen's summation inequality, the auxiliary-function-based summation inequality, and the reciprocally convex matrix inequality, some less conservatism stability criteria for time-varying delayed DNNs are formulated. The validity of the proposed time-varying delay-dependent stability criteria is illustrated by two numerical examples.

In this article, several improved stability criteria for time-varying delayed neural networks (DNNs) are proposed. A degree-dependent polynomial-based reciprocally convex matrix inequality (RCMI) is proposed for obtaining less conservative stability criteria. Unlike previous RCMIs, the matrix inequality in this article produces a polynomial of any degree in the time-varying delay, which helps to reduce conservatism. In addition, to reduce the computational complexity caused by dealing with the negative definite of the high-degree terms, an improved lemma is presented. Applying the above matrix inequalities and improved negative definiteness condition helps to generate a more relaxed stability criterion for analyzing time-varying DNNs. Two examples are provided to illustrate this statement.

The aim of this article is to investigate the stability of sampled-data systems (SDSs) by introducing a sawtooth-characteristic-based hierarchical integral inequality (SCBHII) and to obtain the maximum allowable sampling period that maintains the stability of the system. First, by associating the sawtooth characteristics of the input delay in SDSs with free matrices, an SCBHII is proposed; its accuracy improves as the hierarchy increases. Subsequently, a high-order two-sided looped-functional, which considers both the sampling multi-integral states and the sawtooth pattern, is introduced to cater to the aforementioned inequality. In addition, the system variables are augmented by sawtooth pattern-related terms, which eliminates the need for additional secondary processing when determining the negative-definiteness of derivatives with high-order terms. By combining the high-order two-sided looped-functional with the proposed SCBHII, a stability criterion for SDSs with reduced conservatism is achieved, presented in the form of linear matrix inequalities. The proposed inequality technique and the stability criterion are shown to be effective and superior through three numerical examples and a real-world simplified power market model.

The stability and${\mathcal {H}}_\infty$filtering for delayed discrete-time T-S fuzzy systems are studied in this article. The primary objective is to obtain less conservative and more effective analysis and design methods by exploring a combination of the characteristics of T-S fuzzy systems and the delay-dependent methods. First, as the first step of the Lyapunov–Krasovskii functional (LKF) method, a membership-dependent (MD) LKF with delay-product-type term is established to contain more delay and membership function information. Then, to obtain the negative definite condition of the forward difference of the constructed functional, an MD-matrix-separation-based inequality is developed to obtain tighter estimations for the augmented summation terms and an MD-variable-augmented-based free-weighting matrix method is proposed to avoid the generation of delay-dependent nonlinear terms. Based on the abovementioned methods, a less conservative stability criterion and an${\mathcal {H}}_\infty$fuzzy filter design method are proposed. Finally, the merits of the proposed methods are verified via two examples.

This article concentrates on the fixed-time synchronization (FxTS) problem for fuzzy complex dynamical networks (CDNs) with reaction-diffusion terms and multiple weights. First, a novel fixed-time convergence method is proposed, which relaxes the constraint on the derivative of the constructed Lyapunov functional and incorporates some of the existing results as special cases. Then, an intermittent pinning control scheme is designed to make the state trajectories of all nodes of fuzzy CDNs converge to the equilibrium point within a fixed time, which greatly reduces the control cost. On the basis of the newly presented convergence method and control scheme, several easy-to-verify criteria in the form of linear matrix inequalities are provided to guarantee the FxTS for fuzzy CDNs, and a more accurate estimation of the settling time is obtained. Finally, two examples are given to clarify the correctness of the established theoretical results.

The stability of delayed Takagi–Sugeno fuzzy systems is addressed under membership functions related to time or the system states. In the case where membership functions are correlated with time, improvements are made to existing stability criteria, specifically those reliant solely on the upper bounds of the membership functions' derivative. After constructing the fuzzy Lyapunov–Krasovskii functional, common integral terms are given to compensate for fuzzy integral terms, and free-weighting matrices are incorporated. Consequently, concerned with the unique trait of membership functions, the membership-functions-derivative-dependent stability criteria are derived. These criteria consider both precise upper and lower bounds of the membership functions' derivative, resulting in less conservatism compared with the previous criteria that only contained upper bounds. Moreover, by fully incorporating fuzzy information in the derivatives of fuzzy integral terms, a local stability criterion with reduced conservatism is obtained under membership functions associated with the system states. Ultimately, the efficacy and merits of the presented approach are substantiated through numerical examples.

The focus of this paper is on maintaining the stability and stabilization of Takagi-Sugeno fuzzy systems under conditions of time-delay and sampled-data control. The objective is to introduce stability analysis and synthesis methods that are less conservative. First, a novel sampling point-dependent looped-functional with augmented integral terms is constructed. Then, we propose a matrix-separation-based inequality to obtain a compact estimation for the augmented integral term. Stability and stabilization results with reduced conservatism are obtained based on the above innovative method. The superiority and efficacy of the proposed methods are ultimately demonstrated through the presentation of three examples.

Load frequency control (LFC) is crucial for ensuring the frequency stability of power system, and its control performance is often affected by nonlinearities in devices and multisource-induced hybrid delays in control signal transmission networks. This article investigates the LFC performance analysis and improvement of power systems under the nonlinearities and hybrid delays. First, the nonlinear part is approximated by a Takagi–Sugeno (T–S) fuzzy model and the hybrid delay is divided into two regions, thus establishing a T–S fuzzy LFC model with hybrid delays. Then, based on switched system theory, a delay-dependent weighted$H_\infty$performance analysis criterion for LFC system is proposed, giving the necessary conditions to achieve a certain robustness of the system against disturbances. On this basis, a controller design method is proposed to ensure the system have the optimal level of disturbance rejection under the designed controller. Finally, case studies based on single-area and three-area LFC demonstrate that, compared with previous methods, the proposed method can obtain a larger allowable upper bound of delays and better$H_\infty$performance estimation. Based on this, the designed controller enhances the robust performance of LFC, thereby ensuring the stable operation of power systems under nonlinearities and hybrid delays.

The future power systems with renewable energy sources (RESs) and electric vehicles (EVs) are usually subject to strong uncertainties in system parameters, communication network, and disturbances, which may severely degrade the frequency control performance. This article proposes a performance enhancing load frequency control (LFC) scheme for future power systems with strong uncertainties based on the Kalman-filter (KF) control compensation method. First, the LFC of a multiarea interconnected power system (MAIPS) with RESs and EVs is conceptualized as a linear stochastic and discrete model. Then, KF is introduced to evaluate the unmeasurable states of the LFC, so as to design an additional KF-based state feedback control law. The KF-based control loop serves as compensation for the original controller of the LFC system. Next, an optimal compensation control gain of the KF-based control loop is derived based on a differential optimal calculation method to enhance the control performance of the LFC of MAIPS under strong uncertainties. Finally, simulation results are conducted on a typical three-area LFC systems that integrate RESs and EVs, which demonstrate that the proposed control strategy can provide better control performance and robustness than the original LFC strategy when the systems are subject to strong uncertainties.

This article studies the resilient control against mixed denial of service (DoS) attacks for cyber-physical systems (CPSs). Different from existing results, this work considers the presence of both zero- and hold-input attacks, where a unified model is introduced to describe mixed DoS attacks. Upon this model, the original CPS is reformulated as a switched system subject to a time-varying delay. To characterize the occurrence frequency and duration of zero- and hold-input attacks, the type-dependent average dwell time (ADT) switching is adopted. In the meantime, multiple discontinuous Lyapunov functions (MDLFs) suitable to the type-dependent ADT switching are employed. By virtue of the switching scheme and MDLFs, a piecewise feedback controller is designed to guarantee global uniform exponential stability and$H_\infty$performance of the closed-loop system. In addition, the developed control law is extended to an observer-based version, accommodating the case when the system state is not fully measurable. Finally, the effectiveness of our theoretical results is verified by two numerical examples.

This article investigates the stability of delayed neural networks with large delays. Unlike previous studies, the original large delay is separated into several parts. Then, the delayed neural network is viewed as the switched system with one stable and multiple unstable subsystems. To effectively guarantee the stability of the considered system, the type-dependent average dwell time (ADT) is proposed to handle switches between any two sequences. Besides, multiple Lyapunov functions (MLFs) are employed to establish stability conditions. Adding more delayed state vectors increases the allowable maximum delay bound (AMDB), reducing the conservatism of stability criteria. A general form of the global exponential stability condition is put forward. Finally, a numerical example illustrates the effectiveness, and superiority of our method over the existing one.

The synchronization control for delayed neural networks (DNNs) via a sampled-data controller considering communication delay is studied by input delay approach. Although few scholars have put forward the coexistence of transmission delay and communication delay in this problem, no report has clarified the interaction between transmission delay and communication delay. Also, the time-squared terms are underutilized. Thus, a novel augmented Lyapunov functional, which consists of a mixed-delay-based augmented part and a time-squared two-sided looped part, is proposed to fill this gap. In the mixed-delay-based augmented part, not only the information of transmission delay and communication delay themselves, but also the interaction between those two delays is considered. Time-dependent quadratic terms as well as the sampling integral states are introduced in the two-sided looped part, so that more characteristic information of the sampling pattern is encompassed and the relationship of the states at the sampling instant is enhanced. Then, this novel augmented functional is applied to the synchronization control of DNNs. A less conservative synchronization criterion is obtained in the form of linear matrix inequalities. A numerical example illustrates the validity and superiority of the presented synchronization criterion.

This brief investigates the stability of neural networks with time-varying delays. Novel stability conditions are derived by employing free-matrix-based inequality and introducing the variable-augmented-based free-weighting matrices in the estimation of the derivative of the Lyapunov-Krasovskii functionals (LKFs). Both techniques avoid the appearance of the nonlinear terms of the time-varying delay. Especially, the time-varying free-weighting matrices associated with the derivative of the delay and the time-varying S-Procedure related to the delay and its derivative are combined to improve the presented criteria. Finally, numerical examples are given to illustrate the benefits of the presented methods.

This paper investigates the problem of stability analysis for the uncertain linear systems with time-varying delay. Firstly, an uncertain linear system model considering time-varying delay is established. Then based on the Lyapunov-Krasovskii functional (LKF) method, a novel robust delay-dependent stability criterion is proposed, which is benefited by a new augmented LKF with more effective time-delay information and the use of a tighter integral inequality to estimate functional derivative. The stability criterion obtained is less conservative. At last, a numerical example shows the superiority and effectiveness that the method used in this paper.

This article is concerned with the problem of dissipativity for discrete-time singular systems with time-varying delays. First, the discrete-state decomposition technique is proposed after performing the restricted equivalent transformation for singular systems. To reduce the use of decision variables, the state-decomposed Lyapunov function is established based on the decomposed state vectors. Second, to obtain the condition with less conservatism, the two zero-value equations, especially concerning difference subsystems and algebraic ones, the discrete Wirtinger-based inequality and the extended reciprocally convex inequality are employed to bound the forward difference of the Lyapunov function. Then, the less conservative dissipativity criteria with lower computational complexity are obtained. Finally, simulation results are provided to demonstrate the superiority of the proposed technique.

This article is concerned with passivity analysis of neural networks with a time-varying delay. Several techniques in the domain are improved to establish the new passivity criterion with less conservatism. First, a Lyapunov-Krasovskii functional (LKF) is constructed with two general delay-product-type terms which contain any chosen degree of polynomials in time-varying delay. Second, a general convexity lemma without conservatism is developed to address the positive-definiteness of the LKF and the negative-definiteness of its time-derivative. Then, with these improved results, a hierarchical passivity criterion of less conservatism is obtained for neural networks with a time-varying delay, whose size and conservatism vary with the maximal degree of the time-varying delay polynomial in the LKF. It is shown that the conservatism of the passivity criterion does not always reduce as the degree of the time-varying delay polynomial increases. Finally, a numerical example is given to illustrate the proposed criterion and benchmark against the existing results.

In the case of introducing the double integral state into the augmented vector, the time-varying delay square terms in the derivative of the Lyapunov-Krasovskii functional (LKF) usually needs to be treated with some negative-determination lemmas in the existing literatures, which are only sufficient conditions and are conservative to some extent. In this work, by introducing some new augmented variables, some zero-valued equations are proposed to avoid the appearance of these time-varying delay square terms, which have great potential to reduce the conservatism. Then, a stability result in terms of linear matrix inequalities is derived via the presented zero-valued equations. Finally, a representative example is provided to testify the usefulness and meliority of the raised stability criterion.

This article presents a novel reconstructed model for the delayed load frequency control (LFC) schemes considering wind power, which aims to improve the computational efficiency for PID controllers while retaining their dynamic performance. Via fully exploiting system states influenced by time delays directly, this novel reconstructed method is proposed with a controller isolated. Hence, when the PID controllers are unknown, the stability criterion based on this model can resolve controller gains with less time consumed. For given PID gains, this model can be employed to establish criteria for stability analysis, which can realize the tradeoff between the calculation accuracy and efficiency. The case study is first based on a two-area traditional LFC system to validate the merits of a novel reconstructed model, including accurately estimating the influence of time delay on system frequency stability with increased computational capability. Then, under traditional and deregulated environments, case studies are carried out on the two-area and three-area schemes, respectively. Through the novel reconstructed model, the efficiency of obtaining controller parameters is highly improved while their robustness against the random wind power, tie-line power changes, inertial reductions, and time delays remains almost unchanged.

In this article, the fault detection (FD) filter design problem is addressed for discrete-time memristive neural networks with time delays. When constructing the system model, an event-triggered communication mechanism is investigated to reduce the communication burden and a fault weighting matrix function is adopted to improve the accuracy of the FD filter. Then, based on the Lyapunov functional theory, an augmented Lyapunov functional is constructed. By utilizing the summation inequality approach and the improved reciprocally convex combination method, an FD filter that guarantees the asymptotic stability and the prescribed$H_{\infty }$performance level of the residual system is designed. Finally, numerical simulations are provided to illustrate the effectiveness of the presented results.

The stability of neural networks with a time-varying delay is studied in this article. First, a relaxed Lyapunov-Krasovskii functional (LKF) is presented, in which the positive-definiteness requirement of the augmented quadratic term and the delay-product-type terms are set free, and two double integral states are augmented into the single integral terms at the same time. Second, a new negative-definiteness determination method is put forward for quadratic functions by utilizing Taylor's formula and the interval-decomposition approach. This method encompasses the previous negative-definiteness determination approaches and has less conservatism. Finally, the proposed LKF and the negative-definiteness determination method are applied to the stability analysis of neural networks with a time-varying delay, whose advantages are shown by two numerical examples.

This article is concerned with the stability and stabilization of delayed discrete-time T–S fuzzy systems. The purpose is to develop less conservative stability analysis and state-feedback controller design methods. First, a matrix-separation-based inequality is proposed, which can provide a tighter estimation for the augmented summation term. Then, by constructing a delay-product-type Lyapunov–Krasovskii functional, using the proposed inequality to estimate its forward difference and using a cubic functional negative-determination lemma to handle nonconvex conditions with respect to the delay, a delay and its variation-dependent stability criterion are obtained. Moreover, the corresponding controller design method for closed-loop delayed fuzzy systems is derived via parallel distributed compensation scheme. Finally, two examples are given to demonstrate the effectiveness and merits of the proposed approaches.

This article investigates the admissibility analysis for Takagi–Sugeno fuzzy singular systems (T–S FSSs) with time-varying delays. First, according to the decomposed state vectors, a state decomposition Lyapunov–Krasovskii functional (LKF) is constructed, which possesses fewer decision variables. And, the LKF is augmented by considering more features of the second-order Bessel–Legendre inequality (BLI). Then, the second-order BLI and the generalized reciprocally convex matrix inequality are employed to dispose the derivative of the LKF, where the$d^{2}(t)$-dependent term exists. Meanwhile, by setting an adjustable parameter, the$d^{2}(t)$-dependent term of the condition is handled by a relaxed quadratic function negative-determination condition. As a result, a less conservative admissibility criterion for T–S FSSs is obtained. And, the relationship between the conservatism and the numerical burden is better considered. Finally, a numerical example is given to demonstrate the reduced conservatism and computational complexity.

This article proposesa control performance standard (CPS)-based fuzzy event-triggered scheme for load frequency control (LFC) of power systems with a limited communication bandwidth. First, a CPS-based fuzzy LFC system is established to reduce the wear and tear of the generating unit equipment. Then, based on the Lyapunov stability theory, a stability criterion of the LFC system is proposed to ensure the stable operation of the LFC system, which considers the threshold parameter of the event-triggered condition and the fuzzy gain in the fuzzy LFC system. Next, based on the stability criterion and the Gaussian-type curve-fitting method, a functional expression between the fuzzy gain and the threshold parameter is obtained. According to the expression, the threshold parameter is updated in real time with the change of fuzzy gain, so as to further save usage of the communication network bandwidth. Case studies based on a one-area power system and an IEEE 39-bus benchmark test system are undertaken. Simulation results show that the proposed scheme achieves three objectives: 1) to comply with CPS1 and CPS2 in the North American Electric Reliability Council; 2) to reduce wear and tear of the generating unit equipment; and 3) tosave more communication network resources.

This paper presents an improved stability condition for neural networks with a time-varying delay. In the derivative of Lyapunov-Krasovskii functional (LKF), the non-convex polynomials in the time-varying delay may appear and result in the difficulties for making the derivative of LKF negative-definite. This paper utilizes a negativity-determination method reported recently to handle the non-convex time-varying delay polynomials. The employed method presents necessary and sufficient negativity condition for polynomials. The application of this negativity-determination method to neural networks with a time-varying delay leads to a less conservative stability criterion, which is illustrated with an example.

This paper is concerned with the problem of reachable set estimation for discrete-time Markovian jump neural networks with generally incomplete transition probabilities (TPs). This kind of TP may be exactly known, merely known with lower and upper bounds, or unknown. The aim of this paper is to derive a precise reachable set description for the considered system via the Lyapunov-Krasovskii functional (LKF) approach. By constructing an augmented LKF, using an equivalent transformation method to deal with the unknown TPs and utilizing the extended reciprocally convex matrix inequality, and the free matrix weighting approach to estimate the forward difference of the constructed LKF, several sufficient conditions that guarantee the existence of an ellipsoidal reachable set are established. Finally, a numerical example with simulation results is given to demonstrate the effectiveness and superiority of the proposed results.

Uncertain transmission delays, sampling periods, parameters uncertainties regarding the power system, load fluctuations, and the intermittent generation of renewable energy sources (RESs) will significantly influence a power system's frequency. This article designs a robust delay-dependent PI-based load frequency control (LFC) scheme for a power system based on sampled-data control. First, a sampled-data-based delay-dependent LFC model of power system is constructed. Then, by applying the Lyapunov theory, and the linear matrix inequality technique, a novel stability criterion is developed for the LFC of the power system by considering the sampling period, and transmission delay of the communication network, which ensures that the proposed scheme operates in large sampling periods, and under transmission delays. Next, an exponential decay rate (EDR) is introduced to guide the design of a robust PI-based LFC scheme. The LFC scheme with robustness is designed by setting a small EDR. The values of EDR are adjusted by the given robust performance evaluation conditions of parameter uncertainties, and$H_\infty$performance. Finally, case studies are carried out based on a one-area power system, and a three-area power system with RESs. Simulation results show that the proposed LFC scheme performs strong robustness against parameter uncertainties regarding the power system, and communication network, load fluctuations, and the intermittent generation of RESs.

This article investigates the stability of the switched neural networks (SNNs) with a time-varying delay. To effectively guarantee the stability of the considered system with unstable subsystems and reduce conservatism of the stability criteria, admissible edge-dependent average dwell time (AED-ADT) is first utilized to restrict switching signals for the continuous-time SNNs, and multiple Lyapunov-Kravosikii functionals (LKFs) combining relaxed integral inequalities are employed to develop two novel less-conservative stability conditions. Finally, the numeral examples clearly indicate that the proposed criteria can reduce conservatism and ensure the stability of continuous-time SNNs.

In this article, the problem of filtering is studied for a class of nonlinear systems subject to time delays. The dynamics of nonlinear systems are characterized by Takagi–Sugeno (T–S) affine-fuzzy models. First, an extended bounded real lemma is established. In the process of analysis, a novel membership-dependent Lyapunov–Krasovskii functional is constructed, contributing to reducing the conservatism of the obtained results. Then, a fuzzy filter is designed through a linearization procedure such that the filtering error system is stable and satisfies a specified$H_{\infty }$performance level. The research results further deepen and enrich the theory of fuzzy filtering, providing the theoretical basis and the technical support for real applications. Finally, examples are provided to verify the effectiveness of the developed new design methods.

This paper is concerned with the delay-dependent stability analysis of linear systems with a time-varying delay. Two types of improved Lyapunov-Krasovskii functionals (LKFs) are developed to derive less conservative stability criteria. First, a new delay-product-type LKF, including single integral terms with time-varying delays as coefficients is developed, and two stability criteria with less conservatism due to more delay information included are established for different allowable delay sets. Second, the delay-product-type LKF is further improved by introducing several negative definite quadratic terms based on the idea of matrix-refined-function-based LKF, and two stability criteria with more cross-term information and less conservatism for different allowable delay sets are also obtained. Finally, a numerical example is utilized to verify the effectiveness of the proposed methods.

This article investigates H∞synchronization of delayed neural networks under a receding horizon scheme, where two types of interval time-varying delays are considered according to whether the lower bound of the delay derivative is known or not. Note that a receding horizon synchronization law can be regarded as an optimization solution at each timeslot to a minimaxization problem related closely with a certain cost functional. In this article, two cost functionals with some delay-dependent matrices are introduced, respectively, for the two types of time delays. In order to obtain less conservative conditions, a novel inequality on quadratic polynomial functions is established, which includes some existing ones as its special cases. Based on the novel inequality, two sufficient conditions are derived to design the terminal weighting matrices of the cost functionals such that the resulting synchronization error system can be stabilized with a prescribed infinite horizon H∞performance level. Finally, three numerical examples are used to demonstrate the validity of the proposed results.

This paper is concerned with the stability and stabilization problems of T-S fuzzy systems with time-varying delays. The purpose is to develop a new state-feedback controller design method with less conservatism. First, a novel Lyapunov-Krasovskii functional is constructed by combining delay-product-type functional method together with the state vector augmentation. By utilizing Wirtinger-based integral inequality and an extended reciprocally convex matrix inequality, a less conservative delay-dependent stability condition is developed. Then, the corresponding controller design method for the closed-loop delayed fuzzy system is derived based on parallel distributed compensation scheme. Finally, two classic numerical examples are given to show the effectiveness and merits of the proposed approaches.

In this article, the finite-time H∞state estimation problem is addressed for a class of discrete-time neural networks with semi-Markovian jump parameters and time-varying delays. The focus is mainly on the design of a state estimator such that the constructed error system is stochastically finite-time bounded with a prescribed H∞performance level via finite-time Lyapunov stability theory. By constructing a delay-product-type Lyapunov functional, in which the information of time-varying delays and characteristics of activation functions are fully taken into account, and using the Jensen summation inequality, the free weighting matrix approach, and the extended reciprocally convex matrix inequality, some sufficient conditions are established in terms of linear matrix inequalities to ensure the existence of the state estimator. Finally, numerical examples with simulation results are provided to illustrate the effectiveness of our proposed results.

This paper is concerned with the stubborn state estimation of delayed neural networks that subject to a general class of disturbances in measurements, including outliers and impulsive disturbances as its special cases. This class of disturbances may be unbounded, irregular, and assorted; therefore, they can hardly be suppressed by existing identification-based estimation approaches. In this paper, a stubborn state estimator is constructed by intentionally devising a saturation scheme on the injection of output estimation error. The embedded saturation can effectively resist the influences from these measurement disturbances by saturating them. Moreover, the saturation threshold in the designed scheme is not constant but governed by a dynamic equation with parameters to be designed. Benefiting from this adaptiveness, the estimator obtains more freedom in dealing with various disturbances. By combining a novel Lyapunov functional, the generalized sector condition and two latest integral inequalities, a delay-dependent criterion is derived in a less conservative way to check whether the estimation error system with this dynamic saturation is globally stable. A sufficient condition with two tuning scalars is further provided to codesign the gain of the state estimator and the evolution law of the saturation threshold. Finally, two numerical examples are used to illustrate the stubbornness of this state estimator in the presence of measurement outliers or impulsive disturbances.

This paper studies the dissipativity of singular time-delay systems. The objective is to derive a less conservative criterion with less computational demand. Throughout this paper, the augmented Lyapunov-Krasovskii functional (LKF) and the free-matrix-based integral inequality are used to realize less conservativeness. On the basis of these techniques, a less conservative criterion is first given. Then, by decomposing singular time-delay systems into differential equations and algebraic ones, state vectors of the systems are divided into two parts. To reduce redundant decision variables, each part of the state vectors is considered independently to construct a special augmented LKF with less decision variables. As a result, an improved criterion is deduced, and thus less conservativeness and less computational demand are achieved at the same time. Moreover, the presented state decomposition method provides a new research idea for singular time-delay systems not yet reported in the literatures. Finally, the above statements are demonstrated by a numerical example.

One of the keys for the success of sweep coverage is to organize the participants to patrol effectively in large-scale target areas in order to satisfy the quality requirements of the sweep tasks. In this article, we first analyze the possibility of applying crowdsensing technology for sweep coverage and propose a framework to solve the problem of arranging participants to sweep large-scale target areas when the quality requirements change dynamically over time. First, this problem is formulated as a task assignment problem with the goal of maximizing social welfare. Then, we establish a sweep coverage quality model for the area, which is a different approach from conventional methods that focus on the point of interest (PoI), and we propose a participant incentive model that considers the sustainability of the crowdsensing platform. Since determining the optimal assignment solution is an NP-hard problem, we design two approximate algorithms to arrange participants with the goal of maximizing social welfare; these are the participant-task oriented search (PTOS) algorithm based on a two-stage greed search and the bipartite graph-based participant search (BGPS) algorithm. We evaluate our methods using a population density map dataset from real-world cities as the large-scale target area and create dynamic task requirements for the sweep coverage. The experimental results show that the performance of our two algorithms is significantly better than the performance of the baseline algorithm.

This paper investigates the problem of robust H∞control for a class of nonlinear systems with state and input time-varying delays. The nonlinearity is presented by a continuous-time Takagi-Sugeno (T-S) fuzzy model with parameter uncertainties. A sufficient asymptotic stability condition is first proposed by constructing a delay-product-type augmented Lyapunov-Krasovskii functional and utilizing an extended reciprocally convex matrix inequality together with a Wirtinger-based integral inequality. Then, a state feedback controller is derived that guarantees the closed-loop fuzzy system being asymptotically stable with an H∞performance index. Finally, four numerical examples are given to reveal the effectiveness and merits of the developed new design techniques.

This paper investigates the problem of extended dissipativity for Markovian jump neural networks (MJNNs) with a time-varying delay. The objective is to derive less conservative extended dissipativity criteria for delayed MJNNs. Toward this aim, an appropriate Lyapunov-Krasovskii functional (LKF) with some improved delay-product-type terms is first constructed. Then, by employing the extended reciprocally convex matrix inequality (ERCMI) and the Wirtinger-based integral inequality to estimate the derivative of the constructed LKF, a delay-dependent extended dissipativity condition is derived for the delayed MJNNs. An improved extended dissipativity criterion is also given via the allowable delay sets method. Based on the above-mentioned results, the extended dissipativity condition of delayed NNs without Markovian jump parameters is directly derived. Finally, three numerical examples are employed to illustrate the advantages of the proposed method.

This paper addresses the exponential synchronization problem for neural networks with time-varying delays. First, a novel controller is presented by combining intermittent control with dynamic output feedback control. Next, a sufficient criterion is established based on the Lyapunov-Krasovskii functional approach and the lower bound lemma for reciprocally convex technique to ensure exponential stability of the resultant closed-loop system. Then, some solvable conditions of the proposed control problem are derived in terms of linear matrix inequalities. Notably, our results here extend the existing ones to the relaxed case because the derivative of time-varying delays is now an arbitrary bounded real number. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed method.

This paper is concerned with energy-to-peak state estimation on static neural networks (SNNs) with interval time-varying delays. The objective is to design suitable delay-dependent state estimators such that the peak value of the estimation error state can be minimized for all disturbances with bounded energy. Note that the Lyapunov-Krasovskii functional (LKF) method plus proper integral inequalities provides a powerful tool in stability analysis and state estimation of delayed NNs. The main contribution of this paper lies in three points: 1) the relationship between two integral inequalities based on orthogonal and nonorthogonal polynomial sequences is disclosed. It is proven that the second-order Bessel-Legendre inequality (BLI), which is based on an orthogonal polynomial sequence, outperforms the second-order integral inequality recently established based on a nonorthogonal polynomial sequence; 2) the LKF method together with the second-order BLI is employed to derive some novel sufficient conditions such that the resulting estimation error system is globally asymptotically stable with desirable energy-to-peak performance, in which two types of time-varying delays are considered, allowing its derivative information is partly known or totally unknown; and 3) a linear-matrix-inequality-based approach is presented to design energy-to-peak state estimators for SNNs with two types of time-varying delays, whose efficiency is demonstrated via two widely studied numerical examples.

This brief is concerned with global asymptotic stability of a neural network with a time-varying delay. First, by introducing an auxiliary vector with some nonorthogonal polynomials, a slack-matrix-based integral inequality is established, which includes some existing one as its special case. Second, a novel Lyapunov-Krasovskii functional is constructed to suit for the use of the obtained integral inequality. As a result, a less conservative stability criterion is derived, whose effectiveness is finally demonstrated through two well-used numerical examples.

In networked load frequency control (LFC) systems, time-varying delays could come from two aspects: measurements' transmission from power plant to control center and control signals from the control center to plant side, because of the use of open communication networks. Those delays can affect the dynamic performance and the stability of the system. In this paper, the two delays are considered in one-area LFC system, instead of combining these two delays into one, when the delay-dependent stability analysis is carried out by using Lyaponuvtheory and linear matrix inequality (LMI) technique. Moreover, the dynamic delay interval method is employed to derive less conservative delay-dependent stability criteria for such time-delay system compared with the existing results. Finally, the effectiveness of the proposed criteria are verified by two case studies.

This paper investigates the stability of linear systems with a time-varying delay. We propose a new approach to construct Lyapunuv-Krasovskii functional (LKF). Compared with other traditional approach, the proposed one can provide a higher time-delay upper bound and lower computation complexity. Six stability criteria by linear matrix inequalities (LMIs) are established by proposed two novel LKFs in this paper. Based on one numerical example, the advantages of the proposed approach are illustrated.

This paper is concerned with the stability analysis of discrete-time neural networks with a time-varying delay. Assessment of the effect of time delays on system stability requires suitable delay-dependent stability criteria. This paper aims to develop new stability criteria for reduction of conservatism without much increase of computational burden. An extended reciprocally convex matrix inequality is developed to replace the popular reciprocally convex combination lemma (RCCL). It has potential to reduce the conservatism of the RCCL-based criteria without introducing any extra decision variable due to its advantage of reduced estimation gap using the same decision variables. Moreover, a delay-product-type term is introduced for the first time into the Lyapunov function candidate such that a delay-variation-dependent stability criterion with the bounds of delay change rate is established. Finally, the advantages of the proposed criteria are demonstrated through two numerical examples.

This paper investigates delay-dependent stability for continuous neural networks with a time-varying delay. This paper aims at deriving a new stability criterion, considering tradeoff between conservativeness and calculation complexity. A new Lyapunov-Krasovskii functional with simple augmented terms and delay-dependent terms is constructed, and its derivative is estimated by several techniques, including free-weighting matrix and inequality estimation methods. Then, the influence of the techniques used on the conservativeness and the complexity is analyzed one by one. Moreover, useful guidelines for improving criterion and future work are briefly discussed. Finally, the advantages of the proposed criterion compared with the existing ones are verified based on three numerical examples.

This study deals with the problem of H∞tracking control for a sampled-data networked control system based on a Takagi-Sugeno fuzzy model. An error model is established by combining the input delay and parallel distributed compensation techniques so as to transform the sampling period of a sampler, a signal transmission delay, and data packet dropouts to the refreshing interval of a zero-order hold. The method introduces a new augmented Lyapunov-Krasovskii functional to derive a sufficient condition to ensure a prescribed H∞tracking performance with less conservativeness than others. A fuzzy controller can easily be designed using the condition. A numerical example demonstrates the validity of the method.

The passivity of neural networks with a time-varying delay and norm-bounded parameter uncertainties is investigated in this paper. A complete delay-decomposing approach is employed to construct a Lyapunov-Krasovskii functional. Then, by utilizing a segmentation technique to consider the time-varying delay and its derivative and introducing some free-weighting matrices to express the relationship between the time-varying delay and its varying interval, some improved passivity criteria are derived. Finally, two numerical examples are given to show the effectiveness and the merits of the proposed method.

This paper investigates the delay-dependent stability for generalized continuous neural networks with time-varying delays. A novel Lyapunov-Krasovskii functional (LKF) that considers more information on activation functions of delayed neural networks and delay upper bounds is developed. Simultaneously, most commonly used techniques for treating the derivative of the LKF are reviewed and compared with each other. With the way of introducing slack matrices, those techniques are classified into two categories, including free-weighting matrix (FWM)-based techniques and reciprocally convex combination-based techniques. It is found that the introduced slack matrices play an important role in conservatism reducing and those four types of FWM-based methods lead to same results and are equivalent. Moreover, the obtained criteria are extended to the system with a single time-varying delay. Two numerical examples are given to verify the effectiveness of the proposed method.

This paper deals with the problem of uniform stability and asymptotical stability for nonlinear time delay systems. Some new sufficient conditions are established guaranteeing uniformly stability and asymptotical stability, which show that the derivative of the Lyapunov function relaxes to be indefinite instead of negative definite in the literature. A result for determining input to state stability of nonlinear time delay systems is also reported in this paper.

This paper is concerned with the problem of stability of neural networks with time-varying delays. A novel Lyapunov-Krasovskii functional decomposing the delays in all integral terms is proposed. By exploiting all possible information and considering independent upper bounds of the delay derivative in various delay intervals, some new generalized delay-dependent stability criteria are established, which are different from the existing ones and improve upon previous results. Numerical examples are finally given to demonstrate the effectiveness and the merits of the proposed method.

When modeling the complex economic systems, a target system often need to be categorized into a certain clusters by FCM. The optimal cluster number often is dependent of the selected cluster validity function, but there are so many validity functions proposed, it is difficult to get the optimal cluster number in real target system. A method to get the optimal cluster number of FCM in real systems is proposed: Presets some reasonable cluster numbers, and then chooses a cluster number as the optimal cluster number by some representative validity functions. Testing on the X30 and Bensaid data sets demonstrates the effectiveness and reliability of the proposed method, and finally gives an experiment on Chinapsilas 31 regions according to the level of science and technology (S&T) progress.

This paper addresses the problem of observer-based Hinfincontrol for nonlinear systems with time-varying delay represented by Takagi-Sugeno (T-S) fuzzy model. It presents a single-step linear matrix inequality (LMI) method for the fuzzy control design, which overcomes the drawback of the two-step LMI approach often encountered in the literature. The derivation relies mainly on a proposed matrix decoupling technique using which a resultant matrix inequality can be equivalently converted to strict LMIs. When restricted to delay-free fuzzy systems, the present results improve or reduce to existing ones. Illustrative examples show the effectiveness and merits of the present results.

This correspondence paper focuses on the problem of exponential stability for neural networks with a time-varying delay. The relationship among the time-varying delay, its upper bound, and their difference is taken into account. As a result, an improved linear-matrix-inequality-based delay-dependent exponential stability criterion is obtained without ignoring any terms in the derivative of Lyapunov-Krasovskii functional. Two numerical examples are given to demonstrate its effectiveness.

This paper utilizes soft computing to estimate the effects of production factors on economic growth. Using GA-ISODATA algorithm to categorize China (which contains 31 regions) according to the level of science and technology (S&T), then sets up the fuzzy mapping relation from production factors (fixed assets, human capital and plowland) to economic output, and the result shows that: during the year 1999 to 2003, the effects of the production factors on economic growth are remarkably different in the regions which have dissimilar levels of S&T, the effects of fixed asset, human capital on economy in developed S&T regions are greater than developing or underdeveloped S&T regions, but the effect of plowland in developed S&T regions is less than developing or underdeveloped S&T regions; the effect of human capital on economic growth is greater than fixed assets for all regions; S&T progress and institutional innovation are playing fundamental roles on economic growth.

In this letter, a new method is proposed for stability analysis of neural networks (NNs) with a time-varying delay. Some less conservative delay-dependent stability criteria are established by considering the additional useful terms, which were ignored in previous methods, when estimating the upper bound of the derivative of Lyapunov functionals and introducing the new free-weighting matrices. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method.

This letter is concerned with the stability analysis of neural networks (NNs) with time-varying interval delay. The relationship between the time-varying delay and its lower and upper bounds is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some improved delay/interval-dependent stability criteria for NNs with time-varying interval delay are proposed. Numerical examples are given to demonstrate the effectiveness and the merits of the proposed method.

This correspondence studies the problem of observer-based H infinity control for time-delay Takagi-Sugeno (T-S) fuzzy systems. It provides a delay-dependent linear matrix inequality (LMI)-based method for the control design. It is known that the key important problem in the literature, even for delay-independent case, lies in the difficulty of decoupling matrix variables in corresponding matrix inequalities. This correspondence suggests a decoupling technique for solving matrix inequalities with coupled variables, and provides an LMI-based algorithm by adopting the idea of the cone complementarity problem. The derivation relies on the appropriate choice of Lyaponuv-Krasovskii functionals which incorporate the intersections among local systems. Illustrative examples are given to show the effectiveness of the present delay-dependent result.

A new Lyapunov-Krasovskii functional is constructed for delayed cellular neural networks, and the S-procedure is employed to handle the nonlinearities. An improved global asymptotic stability criterion is also derived that is a generalization of, and an improvement over, previous results. Numerical examples demonstrate the effectiveness of the criterion.

In this letter, the delay-dependent state estimation problem for neural networks with time-varying delay is investigated. A delay-dependent criterion is established to estimate the neuron states through available output measurements such that the dynamics of the estimation error is globally exponentially stable. The proposed method is based on the free-weighting matrix approach and is applicable to the case that the derivative of a time-varying delay takes any value. An algorithm is presented to compute the state estimator. Finally, a numerical example is given to demonstrate the effectiveness of this approach and the improvement over existing ones.