This paper investigates the data-driven H∞performance analysis for event-triggered model-free continuous-time systems by using a data-based expression method. Here, the data-based expression method means that the closed-loop dynamics can be represented by noisy data sequences. First, a data information equation is formulated, where the unknown system matrices can be regarded as its solution. Combined with Lyapunov theory, the data-driven stability conditions and data-driven Zeno-free behavior can be achieved for event-triggered model-free continuous-time systems from noisy data sequences. Also, the derived data-driven conditions can be expressed by both LMIs- (linear matrix inequalities) and algebraic- forms. In contrast with the existing data-driven techniques, the advantages of the proposed method are that the data-driven conditions can be directly derived without establishing pre-appointed form/sizes/structure model-based LMIs conditions in advance. Finally, the results of data-driven method and an application to IEEE 39-bus test system are well discussed and analyzed in contrast with the model-known ideal case.

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 article investigates the problem of bipartite synchronization (BS) for coupled coopetitive memristive neural networks (MNNs) using a switching event-triggered gain-scheduled control strategy. First, a mathematical model of coupled MNNs exhibiting both cooperative and competitive interactions is formulated based on directed signed graph theory. To handle the antagonistic nature of these interactions, an orthogonal transformation is employed to develop a formally unified error system. Then, a switching event-triggered scheme (SETS) is designed, which leverages the coopetitive relationships among nodes to reduce communication costs. Meanwhile, a gain-scheduled controller, which incorporates the cooperative-competitive relationships is designed to achieve the BS. Specifically, the controller consists of both linear and nonlinear components: the linear component ensures system stability, while the nonlinear component compensates for residual terms arising from the heterogeneous structure of MNNs. Furthermore, the nonlinear control gains are scheduled via a function that depends on the error state, its derivative, and the sampled error, thereby reducing the conservatism of the synchronization conditions. A piecewise interval-dependent Lyapunov functional tailored to the characteristics of SETS is constructed. By employing inequality techniques, sufficient conditions for BS are derived in the form of linear matrix inequalities (LMIs), enabling the joint design of the linear control gains and the triggering matrix. To validate the proposed method, both a numerical example and a potential practical application are provided. In addition, two comparative studies are conducted to highlight the advantages of the proposed SETS and the interval-dependent Lyapunov functional, respectively.

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 article is concerned with the secure control problem of memristive neural networks (MNNs) subject to deception attacks. To deal with the influence of deception attacks, a secure control scheme with a memory-dependent event-trigger (MDET) scheme is developed for MNNs while the desired performance can be guaranteed. Here, the MDET scheme is designed to remember the memory characteristic of dynamical process. On this basis, an interval-scheduled looped function (ISLF) is constructed. The feature of ISLF lies in that the positivity of Lyapunov functions can be dropped within the scheduled intervals and the rest are saved. Combined with discrete Lyapunov theory, inequality techniques, and continuous Lyapunov theory, some sufficient conditions are presented to ensure that the closed-loop MNNs are mean-square globally asymptotically stable in the presence of deception attacks. In contrast with the previous works, the improvements of the established trigger scheme and ISLF are well discussed. Lastly, simulation results are carried out to verify the effectiveness of the control scheme.

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 event-triggered synchronization of Lur'e systems subject to actuator saturation. Aiming at reducing control costs, a switching-memory-based event-trigger (SMBET) scheme, which allows a switching between the sleeping interval and the memory-based event-trigger (MBET) interval, is first presented. In consideration of the characteristics of SMBET, a piecewise-defined but continuous looped-functional is newly constructed, under which the requirement of positive definiteness and symmetry on some Lyapunov matrices is dropped within the sleeping interval. Then, a hybrid Lyapunov method (HLM), which bridges the gap between the continuous-time Lyapunov theory (CTLT) and the discrete-time Lyapunov theory (DTLT), is used to make the local stability analysis of the closed-loop system. Meanwhile, using a combination of inequality estimation techniques and the generalized sector condition, two sufficient local synchronization criteria and a codesign algorithm for the controller gain and triggering matrix are developed. Furthermore, two optimization strategies are, respectively, put forward to enlarge the estimated domain of attraction (DoA) and the allowable upper bound of sleeping intervals on the premise of ensuring local synchronization. Finally, a three-neuron neural network and the classical Chua's circuit are used to carry out some comparison analyses and to display the advantages of the designed SMBET strategy and the constructed HLM, respectively. Also, an application to image encryption is provided to substantiate the feasibility of the obtained local synchronization 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 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 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, 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 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.