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 focuses on the problem of $N$ -step model predictive control (MPC) under a mixed time/event-triggered encoding-decoding strategy for polytopic uncertain systems with hard constraints. A staged requirements-dependent mixed time/event-triggered mechanism (MTEM) is proposed. When the system state is outside the terminal constraint set (TCS), the time-triggered pattern is implemented to meet the staged requirement of improving control performance. When the system state is in the TCS, an event-triggered pattern is used to fulfill the staged requirement of conserving resources. The event-triggered pattern contains an adaptively adjusting variable related to the "distance" of the system state from the TCS core, which helps meet the relative staged requirements in the TCS. The staged requirements-dependent MTEM-based encoding-decoding strategy improves the communication security while saving computational resources for encoding and decoding, as well as network resources. Based on two offline optimization problems (OPs), the TCS and the approximate robust one-step sets are designed, respectively. The control laws outside the TCS are obtained by an online OP. A mixed time/event-triggered encoding-decoding-based $N$ -step MPC algorithm is proposed based on three OPs. The algorithm's feasibility and the input-to-state stability of the closed-loop system are analyzed. Two examples are presented to illustrate the effectiveness and superiority of the proposed MTEM and MPC algorithm in saving resources while ensuring control performance.

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 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.

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 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 data communication among sensors, actuators, and controllers in network systems poses various challenges, including packet loss, network-induced delay, and channel noise interference, all of which adversely affect performance of control systems. Based on single-degree-of-freedom (SDOF) controller and two-degree-of-freedom (TDOF) controller, respectively, this article discuss networked control systems (NCSs) with packet loss, network-induced delay, and logarithmic quantization constraints in the communication channel, and proposes a discrete-time modified performance index. By the frequency domain analysis methods and Youla parameterization techniques of controllers, explicit expressions of the modified performance limitations are derived, which quantitatively reveal the impact of the fundamental characteristics of the plant and communication constraints on systems' performance. In addition, a linear dual-freedom vehicle system is modeled and the obtained theorems are applied to verify the correctness of the results. The results show that communication constraints have an adverse impacts on systems' performance, and modified performance index can better measure systems' performance.

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 investigates the leader-following consensus of nonlinear time-delay multiagent system under impulsive control with simultaneous consideration of packet loss and parameter mismatch. Specifically, the inherent parameter mismatch between the leader's dynamics and followers' dynamics is explicitly addressed. To mitigate communication frequency, two novel impulsive control protocols are developed: 1) a pure impulsive scheme for theoretical analysis and 2) a limited impulsive strategy for practical implementation. Furthermore, an auxiliary function is introduced to characterize packet loss phenomena during information transmission, ensuring alignment with real-world communication constraints. By integrating impulsive control theory with reverse average dwell-time analysis, sufficient consensus criteria are rigorously derived for multiagent system with time delays and heterogeneous parameters. Finally some numerical simulations validate the effectiveness of the proposed control framework, demonstrating its capability to achieve consensus under practical communication imperfections.

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 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.

In this article, the problem of multistep model predictive control (MPC) under a mixed time/event-triggered mechanism (MTEM) is investigated for fuzzy systems with hard constraints. To improve its flexibility in adjusting releases, this MTEM incorporates the information from the fuzzy membership functions and the terminal constraint set (TCS). In the online control unit, the time-triggered way is first implemented to steer the system state into the TCS quickly, and then in the offline control unit, the involved event-triggered pattern plays its role in conserving resources while ensuring the control performance. Two offline optimization problems (OPs) are presented to design the TCS and the approximate robust one step sets, respectively, and an online OP is given to design the control laws to steer the system state into TCS. Based on these three OPs, we propose an MTEM-based multistep fuzzy MPC algorithm and demonstrate the feasibility of the algorithm together with the input-to-state stability of the closed-loop system. Three examples are given to verify the effectiveness of the proposed method and its superiority in saving communication and computing resources while ensuring control performance.

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.

This article investigates the multistep model predictive load frequency control problem for multiarea smart grids (MASGs) with wind power and air conditioning loads under false data injection attack, where a control performance standards (CPSs)-dependent dynamic event-triggered mechanism (DETM) is considered to manage the data transmission. The CPSs-dependent DETM contains an adaptive adjustment variable related to two CPSs on the frequency deviation and area control error, which helps it to effectively reduce unnecessary transmission of data packets while promising the required frequency and tie-lie power of the MASGs. Two off-line optimization problems (OPs) are applied to design the terminal constraint set (TCS) and the approximate one step sets, respectively. The control laws designed by an online OP are utilized outside of the TCS. A CPSs-dependent DETM-based multistep MPC algorithm is proposed on the basis of the three OPs. The analyses of the feasibility of the algorithm and the stability of the closed-loop system are given. The effectiveness and superiority of the designed CPSs-dependent DETM and dynamic event-based multistep MPC algorithm are verified in two case studies of two-area and three-area smart grids.

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.

Due to various reasons, outliers, ambient noise and missing data inevitably exist in the industrial processes, and thus the robustness is important when establishing monitoring models. In this study, a robust dissimilarity analytics model (RDAM) is established with Laplace distribution to detect process anomalies in noisy environment. Because of the heavy-tailed characteristic of Laplace distribution, the proposed RDAM method is more robust to ambient noise and outliers when compared to Gaussian distribution-based models. Besides, the missing data problem is also considered and solved in the model development procedure. Using the variational Bayesian inference, the model parameters and latent variables of the RDAM model can be estimated. After that, a monitoring strategy is designed based on the obtained results with both static and dynamic statistics. By this means, both the static deviation of the current sample and the temporal correlation within the process data can be effectively revealed. A simulated example and a real low-pressure heater process are adopted to illustrate the performance of the proposed RDAM method. Specifically, the proposed RDAM method is robust to the ambient noise and missing values, and it has better detection sensitivity for the process anomalies than the selected comparison methods.

The event-triggered model predictive control (MPC) problem is addressed for polytopic uncertain systems. A new dynamic event-triggered mechanism (DETM) with a bounded dynamic variable and a time-varying threshold is proposed to manage measurement data packet releases. The dynamic output-feedback MPC issue is detailed as a "min-max" optimization problem (OP) with an objective function over an infinite horizon, where the hard constraint on the predictive control is required. By applying a Lyapunov-like function containing the bounded dynamic variable, an auxiliary OP constrained by several matrix inequalities is proposed, and the design methods of the output-feedback gains are provided if this auxiliary OP is feasible. The designed MPC controller ensures that the closed-loop system is input-to-state practically stable. Two examples including an event-triggered DC motor are given to illustrate the validity of the developed MPC algorithm. Simulation results verify that the proposed DETM has advantages over some existing triggering mechanisms in decreasing the consumption of resources while meeting the required performance.

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 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 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 investigates the efficient model predictive load frequency control problem for multiarea power systems, where the measured state is transmitted under a new dynamic event-triggered mechanism (DETM) with hybrid variables. By applying$H_{2}$/$H_{\infty }$performance index, a DETM-based efficient model predictive control (EMPC) method is presented. This EMPC issue is described as a “min-max” optimization problem (OP) with hard constraints on system state. By utilizing a Lyapunov function with internal dynamic variable, an offline auxiliary OP with constraints of matrix inequalities is put forward to optimize the feedback gain and the weighting matrix of the DETM. Another offline OP is also proposed to maximize the size of initial feasible region (IFR). To steer the augmented state in IFR into the terminal constraint set and improve the control performance, a sequence of admissible control is implemented whose perturbation parameters are designed by solving an online OP. A case study on a three-area power system demonstrates the validity and superiority of the designed DETM and dynamic event-based EMPC algorithm.

This article investigates the problem of dynamic event-triggered finite-time$H_{\infty }$state estimation for a class of discrete-time nonlinear two-time-scale Markov jump complex networks. A hybrid adjusting variables-dependent dynamic event-triggered mechanism (DETM) is proposed to regulate the releases of measurement outputs of a node to a remote state estimator. Such a DETM contains both an additive dynamically adjusting variable (DAV) and a multiplicative adaptively adjusting variable. The aim is to design a DETM-based mode-dependent state estimator, which guarantees that the resultant error dynamics is stochastically finite-time bounded with$H_{\infty }$performance. By constructing a mode-dependent Lyapunov function with multiple DAVs and a singular perturbation parameter associated with time scales, a matrix-inequalities-based sufficient condition is derived, the feasible solutions of which facilitate the design of the parameters of the state estimator. The validity of the designed state estimator and the superiority of the devised DETM are verified by two examples. It is verified that the devised DETM is capable of saving network resources and simultaneously improving the estimation performance.

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.

Taking into account the infinite distributed delays and reaction-diffusions, this article investigates the global exponential synchronization problem of a class of memristor-based competitive neural networks (MCNNs) with different time scales. Based on the Lyapunov-Krasovskii functional and inequality approach, an adaptive control approach is proposed to ensure the exponential synchronization of the addressed drive-response networks. The closed-loop system is a discontinuous and delayed partial differential system in a cascade form, involving the spatial diffusion, the infinite distributed delays, the parametric adaptive law, the state-dependent switching parameters, and the variable structure controllers. By combining the theories of nonsmooth analysis, partial differential equation (PDE) and adaptive control, we present a new analytical method for rigorously deriving the synchronization of the states of the complex system. The derived m-norm (m ≥ 2)-based synchronization criteria are easily verified and the theoretical results are easily extended to memristor-based neural networks (NNs) without different time scales and reaction-diffusions. Finally, numerical simulations are presented to verify the effectiveness of the theoretical results.

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 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.

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 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 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.

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 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.

A plant is controlled remotely on a network for a networked control system. Disturbances from the network and surroundings may deteriorate the control performance of such a system. To solve this problem, this paper presents a new method of suppressing an exogenous disturbance for those control systems. The control system has a state observer to estimate the state of the plant and an equivalent-input-disturbance (EID) estimator to produce an estimate of the disturbance on the control input channel in a real-time fashion. The system is divided into two subsystems for the analysis of system stability. A stability condition of the control system with a time-varying delay is presented in terms of a linear matrix inequality. Simulations demonstrate the validity of the method. And a comparative study shows the superior of our method to a conventional Smith-EID control method.

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.

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 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 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.