In this study, a standardized controller design and analytical framework is put forward for nonlinear systems that meet the requirements within the framework of full-form iterative dynamic linearization (FFIDL). A discrete data-driven, two-dimensional theoretical analysis method is introduced. This method comprehensively covers both controller and stability analysis under compact form iterative dynamic linearization (CFIDL) and partial form iterative dynamic linearization (PFIDL). Compared with traditional methods, this analysis approach provides a more intuitive and structurally clearer interpretation of the system’s convergence properties. Different from the contraction mapping approach, when excess data tail terms exist, the contraction mapping may readily impede the establishment of closed-loop analysis, thus overlooking valuable data information. In data-based two-dimensional systems, the bounded-input bounded-output (BIBO) properties of contraction mappings are analyzed by using inequalities of two-dimensional expansion in combination with time-weighted functions. Moreover, the limitations related to the full-form dynamic linearization model-free adaptive control (FFDL-MFAC) in the process of tracking constant expectations are addressed. These theoretical and experimental solutions have been verified through simulation results.

This article presents a data-driven control method to address the local asymptotic stabilization problem of discrete-time neural networks (DNNs) under input saturation. To reduce communication load, a memory-type event-triggered mechanism (MEM) is first designed to mitigate the superfluous triggers. Then, a memory-dependent Lyapunov function (MLF) is constructed to accommodate the memory term introduced by the MEM. Based on the designed MEM, the MLF and two data-based system representations, a data-based stabilization criterion is developed, and an estimated region of attraction (ERA) is determined. Simultaneously, the feedback gain and the trigger matrix are co-designed to guarantee the local stability of the closed-loop system. A notable feature of the proposed approach is that the proposed stabilization criteria rely solely on accessible data, without necessitating full knowledge of the system matrices. It makes the approach well-suited for practical applications where precise modeling is difficult or infeasible. Furthermore, a hybrid optimization scheme combining the linear objective minimization method and the particle swarm optimization (PSO) algorithm is presented to maximize the size of the ERA. Finally, two numerical simulations are given to validate the effectiveness of the proposed optimization algorithm, illustrate the influence of data size, and demonstrate the advantages of the designed MEM in stabilizing DNNs.

In this work, a novel PID-type adaptive iterative learning control (AILC) method is proposed for a class of nonlinear systems with unspecified control gain matrices and bounded iterative-varying uncertainties. Unlike the existing iterative learning method with accumulation of control information, the new PID-type AILC avoids control information accumulation in traditional iterative learning control (ILC), maintaining convergence based on error information and confining iteration to parameter estimation, suitable for amplitude- or frequency-limited controllers. Different from the existing approaches of P-type AILC, this work extends ILC advances to PID-type AILC for nonlinear square or nonsquare systems with unknown control gain matrices, enhancing robustness through simultaneous convergence of integral and proportional error terms over a larger range. This analysis method diverges from traditional approaches relying on contraction mappings or asymptotic stability theorems; error convergence is analyzed using inequalities of a composite energy function (CEF). The effectiveness of this work has been validated through two illustrated examples. The results show that compared with P-type AILC, the convergence speed can be increased by approximately two to three times.

This paper raises a predefined-time event-triggered adaptive tracking controller for nonlinear systems with time delays. To mitigate the effects of time-varying delays, a Lyapunov-Krasovskii function is initially introduced. A set of adaptive laws and virtual controllers with switching functions are designed to avoid singularity phenomena. In addition, the event-triggered mechanism with the switching threshold can effectively conserve communication resources while avoiding the occurrence of Zeno behavior. It is theoretically demonstrated that, under the devised control strategy, the system output successfully tracks the reference signal with negligible tracking error within a specified time. Lastly, the validity of the raised control strategy is demonstrated through examples.

This article studies multisynchronization of coupled multistable neural networks (NNs) with directed topology via event-triggered impulsive (ETI) control. At first, the activation function (AF) with${2p}$corners is proposed and it is proved that an n-neuron subnetwork can produce${(p+1)^{n}}$locally stable equilibrium points (EPs) or periodic orbits (POs) under some criteria. Furthermore, to achieve multisynchronization, an ETI controller is designed. Compared with conventional impulsive control strategy, ETI control strategy proposed in this paper can reduce the communication cost and save the bandwidth. Sufficient conditions are given to ensure both dynamical multisynchronization (DMS) and static multisynchronization (SMS) of coupled neural networks (CNNs) with fixed and switching topologies. Moreover, it is proved that the Zeno behavior can be avoided. Lastly, two examples and the application to associative memory are illustrated to testify the validity of the obtained results. Note to Practitioners—ETI control could reduce the number of packets sent as well as the control cost compared with conventional impulsive control. In addition, combining impulsive control with event-triggered schemes into multisynchronization analysis of CNNs is challenging because of the large number of synchronization manifolds in CNNs. Therefore, this research studies multisynchronization of coupled multistable NNs with directed topology via ETI control. A kind of ETI controller is designed and Zeno behavior is avoided. Moreover, the multisynchronization of CNNs is applied to the associative memory for the first time. Compared with the multistability-based associative memory, the multisynchronization-based associative memory can have superiority in resisting the noise interference.

This paper investigates the adaptive event-triggered data-driven control problem for a class of unknown nonlinear discrete networked systems. To address this problem, a stochastic configuration network-based algorithm is developed to construct a candidate mapping set within the modeling-valid domain. Subsequently, an adaptive event-triggered control protocol is proposed, and a closed-loop mapping set is obtained. Then, by leveraging the ideas of transfer stabilization and the S-lemma, a data-driven stability criterion for nonlinear discrete networked systems is derived. The stability criterion solely relies on the data of the controlled system and is independent of both the system model and the data model. Based on this stability criterion, the control gain and triggering matrix of the controlled system can be obtained. Additionally, the effectiveness and practicality of the proposed method are validated through a numerical example and a complex memristive Hopfield neural network circuit.

This paper investigates the bipartite synchronization problem of cooperative-antagonistic neural networks (CANNs) that suffer from hybrid attacks, i.e., denial-of-service (DoS) attacks and replay attacks. A resilient sampled-data control scheme is proposed to deal with the hybrid attacks. In addition, the Laplacian matrix with zero-row-sum is obtained based on the coordinate transformation method. On this basis, an easy-to-handle error system is constructed by integrating the sampling scheme, cooperative-antagonistic interactions and hybrid attacks. Subsequently, an interval-dependent function is designed by considering the characteristics of both replay and DoS attacks. Based on this, using Lyapunov function methods, inequality techniques, and other mathematical skills, some sufficient criteria are obtained for the bipartite synchronization of CANNs. Finally, three algorithms are proposed to minimize the coupling strength, or maximize the replay attack rate or the DoS attack rate, respectively. The effectiveness of the proposed control schemes and the advantages of the interval-dependent function are verified through numerical examples.Note to Practitioners—This work addresses the bipartite synchronization control problem of CANNs, which can be applied to some practical systems such as drone bidirectional formation and team competition. For example, the dynamics of drones within the same formation, including their velocity and position, are consistent with each other but opposite to those of other teams. Additionally, network systems across various industries often encounter DoS attacks or replay attacks during network transmission. A resilient sampled-data control scheme is proposed, and a Lyapunov function dependent on intervals is designed,taking into account the characteristics of the attack. Then, some algorithms are presented to minimize the allowable coupling strength or maximizing the allowable replay attack rate and DoS attack rate. Preliminary simulation experiments indicate that this sampling scheme is feasible. The types of network attacks are diverse. Therefore, obtaining system synchronization control schemes for more complex network attacks is a challenge.

This paper deals with the bipartite synchronization problem of cooperation-competition neural networks (CCNNs) subject to denial-of-service (DoS) attacks. A resilient sampled-data control strategy is proposed to mitigate the adverse impact of DoS attacks, which takes both the attack signal and the periodic sampling communication protocol into account. The directed signed graph is introduced to characterize the cooperation and competition interactions among nodes. By leveraging coordinate transformation and graph theory techniques, a zero-row-sum Laplacian matrix is constructed to facilitate subsequent analysis. In combination with DoS attacks and control strategies, a tractable error system model is formulated. An interval-dependent function is further introduced, taking into account both attack intervals and data transmission intervals. Based on Lyapunov stability theory, the convex combination approach, and inequality techniques, the bipartite synchronization criteria for CCNNs are obtained. Moreover, the constructed interval-dependent function can improve the maximum allowable attack rate or reduce the minimum allowable coupling strength. The proposed control scheme is demonstrated to be effective and superior through the two numerical examples.

This article focus on the quasi-multisynchronization and quasi-monosynchronization of delayed neural networks (DNNs) with parameter mismatch via impulsive control. At first, a kind of actication functions (AFs) is proposed and multistability/monostability criteria of DNNs are given. By judging 2nalgebraic inequalities, then-neuron DNNs with this kind of AFs can produce 2nlocally stable equilibrium points (EPs) or one globally stable EP. In addition, a kind of impulsive controller is designed. Impulsive control strategy proposed in this paper can save the bandwidth and reduce the communication cost compared with continuous-time control strategy. Moreover, the concept of quasi-multisynchronization of DNNs is proposed for the first time and sufficient conditions are given to ensure quasi-multisynchronization and quasi-monosynchronization of DNNs by building the comparison system and using the Lagrange method of variation of parameters. Under this control method, a monostable system can become a multistable system, which means that the storage capacity (SC) of DNNs is improved. Lastly, two examples are illustrated to testify the validity of the proposed theory and method.

This article investigates the global stabilization problem for a class of nonlinear systems via adaptive event-triggered output-feedback control. The distinguishing feature of the system mainly lies in the unknown control coefficient, the unknown growth rate (UGR) with polynomial-of-output growth (POG), the external disturbances and the unmeasurable states. In order to handle the above uncertainties, a dynamic high-gain and a high-gain-based observer are introduced. Aiming at reducing the computational costs and saving the communication resources, a dynamic event-triggering mechanism (ETM) is provided. An event-triggered controller based on the observer and the dynamic high-gain is designed by the technique of the backstepping and the method of the universal control. It can ensure global boundedness of all the closed-loop system states, and meanwhile, the Zeno behavior is avoided. A practical example is given to illustrate the correctness of the proposed method.

This paper investigates the security control of a class of discrete-time Markov jump systems (DMJS). Due to the vulnerability of open communication networks to cyber attacks, a hybrid attack model is established to describe the situation where the DMJS is simultaneously suffered from deception attacks (DAs) and denial-of-service (DoS) attacks. To cope with the intermittent characteristic of DoS attacks, adaptive memory-based event-triggered control (AMETC) with a switching-like adaptive law is proposed. The designed AMETC includes historical triggered data in its triggering condition, hence allows data transmission to adjust adaptively based on the long-term change of system state. In addition, when DoS attacks are launched by attackers, the designed switching-like adaptive law can help decrease the threshold to trigger more sampled data so as to stabilize the DMJS. These features contribute to improve the tolerance of the whole control system to DoS attacks and DAs. On the basis of the AMETC, a novel Lyapunov functional is designed, and sufficient conditions are derived to ensure the asymptotic stability of DMJSs. This functional plays a crucial role in ensuring the negative definiteness of the LMIs in the stability condition. Based on the stability condition, a design algorithm for security control gains and event-trigger matrices is given. Finally, simulation results validate the effectiveness and superiority of the proposed mechanism.Note to Practitioners—This paper was motivated by existing results on memory-based event-triggered control (METC) and hybrid cyber attacks. The aim of this paper is to design a novel AMETC with a switching-like adaptive law to cope with the impact of hybrid attacks on system performance. In practical applications, if the event-triggered mechanism only considers the transient information of the system, it may lead to high peak responses of the control systems, resulting in a decrease in system performance. Therefore, the AMETC proposed in this paper considers both the transient information and the long-term state change of the system. It can adjust the data transmission rate adaptively and save transmission resources effectively. Additionally, based on the designed AMETC, sufficient conditions are obtained to ensure the safe and stable operation of DMJSs. Our theoretical analysis and simulation results show the effectiveness and superiority of the designed mechanism.

This paper focuses on the exponential stabilization issue of networked Lur’e systems (NLSs) suffering from DoS attacks. To conserve limited network resources and withstand aperiodic DoS attacks, a resilient memory-based event-trigger (RMET) mechanism is firstly designed. Then, based on an in-depth discussion on the relationship between the RMET scheme and DoS attacks, a comprehensive closed-loop system mathematical model is established. The model describes a clear switching characteristic of the whole control loop among waiting intervals, detection intervals, and DoS attacking intervals. On this basis, two multi-interval-dependent Lyapunov functionals (MIDLFs) are constructed. The primary advantage of the MIDLFs is that they can effectively exploit the information contained within the waiting intervals and DoS attacking intervals. Subsequently, an exponential stability criterion is derived by virtue of the continuity of the designed MIDLFs and the application of various inequality estimation techniques. Additionally, a co-design algorithm associated with the secure feedback gain and the event-trigger (ET) matrix is carried out. Finally, two numerical simulations are utilized to confirm the benefits of the RMET mechanism and MIDLFs in reducing the number of data packets as well as enhancing the tolerance ability of DoS attacks, respectively.

This paper investigates the secure synchronization control of Markovian jump neural networks (MJNNs) suffering from denial of service attacks (DoS attacks). The issue is presented for two reasons: 1) multiple sensors are generally used to measure the information of different state variables in practical networked control systems; 2) DoS attacks will disrupt the transmission of data packets in communication channels, thereby causing the system performance degradation. To deal with these problems, a multi-sensor-based switching event-triggered mechanism (SETM) is designed. More specifically, when the data packets are transmitted normally, the SETM will switch to an adaptive memory-based event-triggered mechanism, thereby saving the network resources. When the DoS attack occurs, the SETM will trigger immediately at the end of the DoS attack to improve the system performance. To facilitate the stability analysis, a merging time series is constructed by integrating the triggering instants of successful transmission and the ending instants of DoS attacks together. In light of the merging time series, a switched closed-loop system is established. Then, by utilizing the stability analysis idea of switched systems, a multiple Lyapunov functional is constructed, enabling the exploitation of multi-sampling. On this basis, a synchronization criterion is derived, accompanied by a co-design method for controller and the trigger matrices. Finally, the outcomes of the simulation confirm both the efficacy and the advantage of the suggested approach, especially when dealing with DoS attacks.

This article studies the$H_\infty$exponential synchronization problem of delayed chaotic Lur'e systems (DCLSs). Considering the case of sensors sampling with different periods, an asynchronous memory-based event-triggered scheme is proposed to deal with the multiple sampling periods cases. To be specific, a group of memory-based event-triggered processors with different triggering conditions are set behind the sensors. Such a scheme supports the sensors to sample with different periods and supports the packets arrive at the controller side asynchronously. Then, to develop the closed-loop system, a merging time sequence$\lbrace t_{s}\rbrace$is constituted by using the release instants and by considering the transmission delays. On this basis, a so-called multirate Lyapunov functional is constructed, which including the information of the sampling upper bounds of different sensors. Furthermore, two criteria for$H_\infty$exponential synchronization of DCLSs are derived in the form of linear matrix inequalitys (LMIs). And, the controller gain can be obtained from the feasible solution of the LMIs. And, a numerical example is provided to demonstrate the effectiveness and merits of the proposed method.

This article investigates the sampled-data-based secure synchronization control problem for chaotic Lur'e systems subject to power-constrained denial-of-service (DoS) attacks, which can block data packets' transmission in communication channels. To eliminate the adverse effects, a resilient sampled data control scheme consisting of a secure controller and communication protocol is designed by considering the attack signals and periodic sampling mechanism simultaneously. Then, a novel index, i.e., the maximum anti-attack ratio, is proposed to measure the secure level. On this basis, a multi-interval-dependent functional is established for the resulting closed-loop system model. The main feature of the developed functional lies in that it can fully use the information of resilient sampling intervals and DoS attacks. In combination with the convex combination method, discrete-time Lyapunov theory, and some inequality estimate techniques, two sufficient conditions are, respectively, derived to achieve sampled-data-based secure synchronization of drive-response systems against DoS attacks. Compared with the existing Lyapunov functionals, the advantages of the proposed multi-interval-dependent functional are analyzed in detail. Finally, a synchronization example and an application to secure communication are provided to display the effectiveness and validity of the obtained results.

This article is concerned with the local stabilization of neural networks (NNs) under intermittent sampled-data control (ISC) subject to actuator saturation. The issue is presented for two reasons: 1) the control input and the network bandwidth are always limited in practical engineering applications and 2) the existing analysis methods cannot handle the effect of the saturation nonlinearity and the ISC simultaneously. To overcome these difficulties, a work-interval-dependent Lyapunov functional is developed for the resulting closed-loop system, which is piecewise-defined, time-dependent, and also continuous. The main advantage of the proposed functional is that the information over the work interval is utilized. Based on the developed Lyapunov functional, the constraints on the basin of attraction (BoA) and the Lyapunov matrices are dropped. Then, using the generalized sector condition and the Lyapunov stability theory, two sufficient criteria for local exponential stability of the closed-loop system are developed. Moreover, two optimization strategies are put forward with the aim of enlarging the BoA and minimizing the actuator cost. Finally, two numerical examples are provided to exemplify the feasibility and reliability of the derived theoretical results.

This article is concerned with the integral-type event-triggered stabilization problem for Tahaki–Sugeno (T–S) fuzzy systems by employing the preassigned-interval looped function method. Herein, preassigned-interval looped function means that the positivity and symmetry on Lyapunov functions are removed in the inner preassigned intervals. The rest are saved. First, an integral-type trigger scheme is proposed to remember the evolution information of systems, which contributes to sampling the really necessary data packets. Then, a novel Lyapunov function is designed by using the integral of state information and preassigned intervals. In combination with some inequality techniques, continuous-time Lyapunov theory (CLT) and discrete-time Lyapunov theory (DLT), two sufficient conditions are developed to ensure the T–S fuzzy systems can be stabilized to the origin in the presence of an integral-type trigger scheme. Compared with some existing results, the advantages of the preassigned-interval looped function and trigger scheme are well analyzed. Finally, simulation results are carried out to verify the effectiveness of the control scheme.

This article is concerned with the exponential stabilization of switched neural networks (SNNs) with asynchronous switching. To save the limited bandwidth effectively, an adaptive periodic event-triggered mechanism (APETM) with a novel adaptive rule is excogitated, in which the threshold function is updated at each sampling instant to quickly respond to system changes and a tuning parameter is introduced to increase the adjustable range of the threshold function. A merging signal is constructed and then the closed-loop system is established to carry out stability analysis for asynchronous and synchronous switching cases within a unified framework. Then, based on the merging signal, a corresponding Lyapunov functional that includes a looped functional is constructed. This looped functional helps to reduce conservatism of the stability criterion. Finally, examples, including relevant discussions and comparisons, are shown to illustrate the efficacy of our developed results.

This paper addresses the bipartite leader-follower synchronization (BLFS) of cooperation-competition neural networks (CCNNs) via sampled-data (SD) control. First, the directed signed graph (SG) theory is applied to describe the cooperation and competition interactions, and thus, an appropriate mathematical model is constructed for such kind of multiple CCNNs. Based on the coordinate transformation technique, the main challenges encountered from the Laplacian matrix of the directed SG are circumvented. Then, a tractable error system can be established in the presence of SD control. Two interval-scheduled looped-functions are well-structured by relaxing the requirements of positive definiteness and continuity, respectively. In combination with discrete Lyapunov theory and some inequality techniques, some less conservative criteria are derived to guarantee the BLFS of CCNNs. Compared with the previous analysis methods, a smaller coupling strength or a larger sampling interval can be permitted on the basis of the developed results. Finally, two examples are presented to verify the effectiveness and advantages of the obtained results.

This article is concerned with the local stabilization of memristive neural networks subject to actuator saturation via aperiodic sampled-data control. A dynamic partitioning point is elegantly introduced, which is placed between the latest sampling instant and the present time to utilize more information of the inner sampling. To analyze the stability of the closed-loop system, a time-dependent two-side looped functional, which fully utilizes the state information on the entire sampling interval as well as at the dynamic partitioning point, is constructed. It relaxes the positive definiteness of traditional Lyapunov functional inside the sampling interval and therefore, provides the possibility to derive less conservative stability results. Besides, an auxiliary system is established to describe the dynamics at the partitioning point. On the basis of the constructed looped functional, the discrete-time Lyapunov theorem, and some estimation approaches, a linear matrix inequalities-based stability criterion is developed, and then, the sampled-data saturated controller is designed to ensure the local asymptotic stability of the closed-loop system. Thereafter, two optimization problems are developed to seek the desired feedback gain and to expand the estimation of the region of attraction or to enlarge the upper bound of the sampling interval. Eventually, a numerical example is given to demonstrate the effectiveness and the superiority of the proposed results.

This article is concerned with the resilient sampled-data control for stabilization of Tahaki--Sugeno (T--S) fuzzy systems in the presence of denial-of-service (DoS) attacks. To describe the effects of DoS attacks, an appropriate mathematical model is established to characterize the complicated dynamical behaviors of DoS attacks and periodic sampling mechanism. On this basis, a resilient sampled-data control scheme including communication protocols and security controller gains, is proposed to account for the effects of DoS attacks. Meanwhile, a novel index is developed to measure the antiattack ability and security level. By utilizing the information of DoS attacks and resilient sampling intervals, a continuous interval-dependent Lyapunov function is constructed which does not increase at the resilient sampling instants. Then, according to the designed interval-dependent function, several inequalities estimation techniques, convex combination approach, and together with discrete-time Lyapunov theory, two sufficient criteria are derived to guarantee that the closed-loop T--S fuzzy systems are globally asymptotically stable with prespecified security levels subject to DoS attacks. The advantages of designed function are well analyzed in contrast with the previous discontinuous Lyapunov functionals. At last, two simulation examples are given to demonstrate the validity and effectiveness of the obtained results.

In this article, the local stabilization problem is investigated for a class of memristive neural networks (MNNs) with communication bandwidth constraints and actuator saturation. To overcome these challenges, a discontinuous event-trigger (DET) scheme, consisting of the rest interval and work interval, is proposed to cut down the triggering times and save the limited communication resources. Then, a novel relaxed piecewise functional is constructed for closed-loop MNNs. The main advantage of the designed functional consists in that it is positive definite only in the work intervals and the sampling instants but not necessarily inside the rest intervals. With the aid of extended reciprocally convex combination lemma, generalized sector condition, and some inequality techniques, two local stabilization criteria are established on the basis of both the discrete- and continuous-time Lyapunov methods. The proposed analysis technique fully takes advantage of the looped-functional and the event-trigger mechanism. Moreover, two optimization schemes are, respectively, established to design the control gain and enlarge the estimates of the admissible initial conditions (AICs) and the upper bound of rest intervals. Finally, some comparison results are given to validate the superiority of the proposed method.

In this article, the exponential synchronization of Markovian jump neural networks (MJNNs) with time-varying delays is investigated via stochastic sampling and looped-functional (LF) approach. For simplicity, it is assumed that there exist two sampling periods, which satisfies the Bernoulli distribution. To model the synchronization error system, two random variables that, respectively, describe the location of the input delays and the sampling periods are introduced. In order to reduce the conservativeness, a time-dependent looped-functional (TDLF) is designed, which takes full advantage of the available information of the sampling pattern. The Gronwall-Bellman inequalities and the discrete-time Lyapunov stability theory are utilized jointly to analyze the mean-square exponential stability of the error system. A less conservative exponential synchronization criterion is derived, based on which a mode-independent stochastic sampled-data controller (SSDC) is designed. Finally, the effectiveness of the proposed control strategy is demonstrated by a numerical example.

In this article, a memory-based event-trigger (MBET) scheme is designed to investigate the global synchronization problem of a class of Lur’e systems. There are two reasons for presenting this issue: 1) most of the existing event-trigger schemes do not take the historical state information into account and, therefore, may have some conservatism in reducing the number of triggering times and 2) the existing Lyapunov functionals cannot be directly utilized in the stability analysis of the resulting closed-loop system in this article. Motivated by the above-mentioned considerations, an MBET scheme, in which a time-memory term and an exponential decaying term are incorporated into the threshold function, is newly designed. It is beneficial to enlarging the intertrigger intervals and, thus, can further reduce the transmission of sampled data packets. Taking the features of MBET into consideration, a novel piecewise but continuous functional is constructed. On this basis, Lyapunov stability theory and some inequality estimation techniques are used to develop three linear matrix inequalities (LMIs)-based synchronization criteria and, meanwhile, a co-design for the control gain and the triggering matrix is carried out. Finally, some comparative analyses are provided to demonstrate the advantages of the MBET through an example of Chua’s circuit. Also, the application to information safety is given to verify the effectiveness of the synchronization results by using a 3-neuron neural network.

This article addresses the quasi-synchronization problem of delayed memristive neural networks (MNNs) via hybrid event-triggered control. First, a hybrid event-triggering mechanism with a novel threshold function is devised. Therein, an exponential decay term and a non-negative constant term are additionally introduced. It can further extend the time span between two successively triggered events and therefore can reduce the amount of triggering times in comparison with some existing event-triggering mechanisms. Then, by constructing a time-dependent and piecewise Lyapunov functional, a less conservative criterion for quasi-synchronization of drive-response delayed MNNs is formulated in terms of linear matrix inequalities. In addition, an explicit expression of the error bound is provided and the design of the feedback gain is presented for a predetermined error bound. Finally, a numerical example is given to demonstrate the effectiveness of the theoretical analysis and the advantages of the proposed event-triggering scheme.

This paper addresses the global stabilization of fractional-order memristor-based neural networks (FMNNs) with time delay. The voltage threshold type memristor model is considered, and the FMNNs are represented by fractional-order differential equations with discontinuous right-hand sides. Then, the problem is addressed based on fractional-order differential inclusions and set-valued maps, together with the aid of Lyapunov functions and the comparison principle. Two types of control laws (delayed state feedback control and coupling state feedback control) are designed. Accordingly, two types of stabilization criteria [algebraic form and linear matrix inequality (LMI) form] are established. There are two groups of adjustable parameters included in the delayed state feedback control, which can be selected flexibly to achieve the desired global asymptotic stabilization or global Mittag-Leffler stabilization. Since the existing LMI-based stability analysis techniques for fractional-order systems are not applicable to delayed fractional-order nonlinear systems, a fractional-order differential inequality is established to overcome this difficulty. Based on the coupling state feedback control, some LMI stabilization criteria are developed for the first time with the help of the newly established fractional-order differential inequality. The obtained LMI results provide new insights into the research of delayed fractional-order nonlinear systems. Finally, three numerical examples are presented to illustrate the effectiveness of the proposed theoretical results.

We study the problem of master-slave synchronization of two delayed memristive neural networks (MNNs). Different from most previous papers, memristors are regarded as uncertain continuous time-varying parameters, and MNNs are modeled by neural networks (NNs) with continuous time-varying parameters and polytopic uncertainty. Thus, synchronization of two delayed MNNs is converted into synchronization of delayed NNs with uncertain parameter mismatches. Quasi-synchronization criteria are derived by Lyapunov function and inequality technique. It is shown that, given a predetermined error bound, quasi-synchronization of two delayed chaotic MNNs can be achieved provided that the pinning strength is larger than a threshold. In the end, a numerical example is provided to illustrate the effectiveness of the derived results.

This paper is concerned with quasi-synchronization of delayed memristive neural networks (MNNs) with switching jumps mismatches via aperiodically intermittent control. The issue is presented for three reasons: 1) the existing controllers for synchronization may be too complicated and not economical; 2) under the influence of switching jumps mismatches, synchronization of MNNs may fail to achieve; and 3) matrix measure method is less conservative but cannot be applied directly to synchronization of MNNs. To overcome these difficulties, the concept of asynchronously switching time interval is proposed to describe the phenomenon when the drive-response MNNs switch their connection weights asynchronously. Then, aperiodically intermittent control is designed and quasi-synchronization analysis is carried out based on a combined method that compromises the merits of interval matrix method and matrix measure method. A quasi-synchronization criterion, expressed in terms of the mixture of p-norm and matrix measure of the memristive connection weights, is established. Meanwhile, the fundamental reason for the failure of complete synchronization is revealed. Moreover, an explicit expression of the error level is obtained and the design of the controller under a predetermined error level is presented. The obtained results in this paper reduce the conservativeness and provide a novel insight into the research of synchronization of MNNs.