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The existing impulsive consensus algorithms for second-order Lipschitz nonlinear multi-agent systems require to apply the impulsive control to both position and velocity vectors at the same time. Such a requirement cannot be met in most of the real-world applications. To overcome the limitations of these impulsive algorithms, two kinds of new second-order impulsive consensus algorithms using only velocity regulation are proposed. Through developing a weighted discontinuous Lyapunov function-based approach that is able to leverage the spectral property of Laplacian matrix, impulse-dwell-time-dependent sufficient conditions for solving second-order impulsive consensus are derived in the form of linear matrix inequalities. Further, it is shown that if the impulsively controlled velocity subsystems are globally exponentially stable, the impulsive static consensus algorithm is able to ensure that all agents tend to an agreed position. Based on the consensus conditions, two convex optimization problems are formulated, by which the impulsive gain matrices for ensuring a prescribed exponential convergence rate can be designed. Finally, the effectiveness of the proposed distributed impulsive consensus algorithms is certified through numerical simulations.

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This article revisits the problems of impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks (DDNNs) in the presence of disturbance in the input channel. A new Lyapunov approach based on double Lyapunov functionals is introduced for analyzing exponential input-to-state stability (EISS) of discrete impulsive delayed systems. In the framework of double Lyapunov functionals, a pair of timer-dependent Lyapunov functionals are constructed for impulsive DDNNs. The pair of Lyapunov functionals can introduce more degrees of freedom that not only can be exploited to reduce the conservatism of the previous methods, but also make it possible to design variable gain impulsive controllers. New design criteria for impulsive stabilization and impulsive synchronization are derived in terms of linear matrix inequalities. Numerical results show that compared with the constant gain design technique, the proposed variable gain design technique can accept larger impulse intervals and equip the impulsive controllers with a stronger disturbance attenuation ability. Applications to digital signal encryption and image encryption are provided which validate the effectiveness of the theoretical results.

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This paper is concerned with the positivity and impulsive stabilization of equilibrium points of delayed neural networks (DNNs) subject to bounded disturbances. With the aid of the continuous dependence theorem for impulsive delay differential equations, a relaxed positivity condition is derived, which allows the neuron interconnection matrix to be Metzler if the activation functions satisfy a certain condition. The notion of input-to-state stability (ISS) is introduced to characterize internal global stability and disturbance attenuation performance for impulsively controlled DNNs. The ISS property is analyzed by employing a time-dependent max-separable Lyapunov function which is able to capture the positivity characterization and hybrid structure of the considered DNNs. A ranged dwell-time-dependent ISS condition is obtained, which allows to design an impulsive control law via partial state variables. As a byproduct, an improved global exponential stability criterion for impulse-free positive DNNs is obtained. The applicability of the achieved results is illustrated through three numerical examples.

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This article investigates the asynchronous proportional-integral observer (PIO) design issue for singularly perturbed complex networks (SPCNs) subject to cyberattacks. The switching topology of SPCNs is regulated by a nonhomogeneous Markov switching process, whose time-varying transition probabilities are polytope structured. Besides, the multiple scalar Winner processes are applied to character the stochastic disturbances of the inner linking strengths. Two mutually independent Bernoulli stochastic variables are exploited to characterize the random occurrences of cyberattacks. In a practical viewpoint, by resorting to the hidden nonhomogeneous Markov model, an asynchronous PIO is formulated. Under such a framework, by applying the Lyapunov theory, sufficient conditions are established such that the augmented dynamic is mean-square exponentially ultimately bounded. Finally, the effectiveness of the theoretical results is verified by two numerical simulations.

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This article addresses the scaled consensus problem for a class of heterogeneous multiagent systems (MASs) with a cascade-type two-layer structure. It is assumed that the information of the upper layer state components is intermittently exchangeable through a strongly connected communication network among the agents. A distributed hierarchical hybrid control framework is proposed, which consists of a lower layer controller and an upper layer one. The lower layer controller is a decentralized continuous feedback controller, which makes the lower layer state components converge to their target values. The upper layer controller is a distributed impulsive controller, which enforces a scaled consensus for the upper layer state components. It is proved that the two layer controllers can be designed separately. By considering the dwell-time condition of impulses and the feature of the strongly connected Laplacian matrix, a novel weighted discontinuous function is constructed for scaled consensus analysis. By using the Lyapunov function, a sufficient condition for scaled consensus of the MAS is derived in terms of linear matrix inequalities. As an application of the proposed distributed hybrid control strategy, a relaxed distributed hybrid secondary control algorithm for dc microgrid is obtained, by which the balance requirement on the communication digraph is removed, and an improved current sharing condition is obtained.

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In this paper, a time-scale-dependent coupling scheme for two-time-scale nonlinear complex networks is proposed. According to this scheme, the inner coupling matrices are related to the fast dynamics of individual subsystems, but are no longer time-scale-independent. Designing time-scale-dependent inner coupling matrices is motivated by the fact that the difference of time scales is an essential feature of modular architecture of two-time-scale systems. Under the novel coupling framework, the previous assumption on individual two-time-scale subsystems that the fast dynamics must be exponentially stable can be removed. The idea of time-scale separation is employed to analyze the stability of synchronization error systems via weighted ε -dependent Lyapunov functions. For a given upper bound of the singular perturbation parameter ε , it is proved that the exponential decay rate of the synchronization error can be guaranteed to be independent of the value of ε . In this way, criteria for local and global exponential synchronization are established. The allowable upper bound of ε such that the synchronizability of the considered two-time-scale network is retained can be obtained by solving a set of ε -dependent matrix inequalities. Finally, the efficiency of the proposed time-scale-dependent coupling strategy is demonstrated through numerical simulations.

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This paper proposes an event-triggered control framework, called dual-stage periodic event-triggered control (DSPETC), which unifies periodic event-triggered control (PETC) and switching event-triggered control (SETC). Specifically, two period parameters h1 and h2 are introduced to characterize the new event-triggering rule, where h1 denotes the sampling period, while h2 denotes the monitoring period. By choosing some specified values of h2, the proposed control scheme can reduce to PETC or SETC scheme. In the DSPETC framework, the controlled system is represented as a switched system model and its stability is analyzed via a switching-time-dependent Lyapunov functional. Both the cases with/without network-induced delays are investigated. Simulation and experimental results show that the DSPETC scheme is superior to the PETC scheme and the SETC scheme.

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This paper presents a new impulsive synchronization criterion of two identical reaction-diffusion neural networks with discrete and unbounded distributed delays. The new criterion is established by applying an impulse-time-dependent Lyapunov functional combined with the use of a new type of integral inequality for treating the reaction-diffusion terms. The impulse-time-dependent feature of the proposed Lyapunov functional can capture more hybrid dynamical behaviors of the impulsive reaction-diffusion neural networks than the conventional impulse-time-independent Lyapunov functions/functionals, while the new integral inequality, which is derived from Wirtinger's inequality, overcomes the conservatism introduced by the integral inequality used in the previous results. Numerical examples demonstrate the effectiveness of the proposed method. Later, the developed impulsive synchronization method is applied to build a spatiotemporal chaotic cryptosystem that can transmit an encrypted image. The experimental results verify that the proposed image-encrypting cryptosystem has the advantages of large key space and high security against some traditional attacks.

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In this paper, multistability analysis for a class of stochastic delayed Hopfield neural networks is investigated. By considering the geometrical configuration of activation functions, the state space is divided into 2(n) + 1 regions in which 2(n) regions are unbounded rectangles. By applying Schauder's fixed-point theorem and some novel stochastic analysis techniques, it is shown that under some conditions, the 2(n) rectangular regions are positively invariant with probability one, and each of them possesses a unique equilibrium. Then by applying Lyapunov function and functional approach, two multistability criteria are established for ensuring these equilibria to be locally exponentially stable in mean square. The first multistability criterion is suitable to the case where the information on delay derivative is unknown, while the second criterion requires that the delay derivative be strictly less than one. For the constant delay case, the second multistability criterion is less conservative than the first one. Finally, an illustrative example is presented to show the effectiveness of the derived results.

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This paper investigates the problems of impulsive stabilization and impulsive synchronization of discrete-time delayed neural networks (DDNNs). Two types of DDNNs with stabilizing impulses are studied. By introducing the time-varying Lyapunov functional to capture the dynamical characteristics of discrete-time impulsive delayed neural networks (DIDNNs) and by using a convex combination technique, new exponential stability criteria are derived in terms of linear matrix inequalities. The stability criteria for DIDNNs are independent of the size of time delay but rely on the lengths of impulsive intervals. With the newly obtained stability results, sufficient conditions on the existence of linear-state feedback impulsive controllers are derived. Moreover, a novel impulsive synchronization scheme for two identical DDNNs is proposed. The novel impulsive synchronization scheme allows synchronizing two identical DDNNs with unknown delays. Simulation results are given to validate the effectiveness of the proposed criteria of impulsive stabilization and impulsive synchronization of DDNNs. Finally, an application of the obtained impulsive synchronization result for two identical chaotic DDNNs to a secure communication scheme is presented.

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This paper presents new complete stability results for delayed cellular neural networks (DCNNs). A novel method is proposed for complete stability analysis of DCNNs. By applying the M-matrix theory and introducing some new estimation techniques on the solutions of DCNNs, a simple and improved complete stability criterion is derived. The new criterion unifies the delay-dependent and delay-independent complete stability conditions for DCNNs. Moreover, the obtained delay-dependent criterion can give a larger upper bound of the time delay than the existing ones such that the complete stability can still be retained. Numerical examples are presented which show that the new complete stability results for DCNNs are compared favorably with the existing results.

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This brief investigates the problem of mean square exponential stability of uncertain stochastic delayed neural networks (DNNs) with time-varying delay. A novel Lyapunov functional is introduced with the idea of the discretized Lyapunov-Krasovskii functional (LKF) method. Then, a new delay-dependent mean square exponential stability criterion is derived by applying the free-weighting matrix technique and by equivalently eliminating time-varying delay through the idea of convex combination. Numerical examples illustrate the effectiveness of the proposed method and the improvement over some existing methods.

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This brief is concerned with asymptotic stability of neural networks with uncertain delays. Two types of uncertain delays are considered: one is constant while the other is time varying. The discretized Lyapunov-Krasovskii functional (LKF) method is integrated with the technique of introducing the free-weighting matrix between the terms of the Leibniz-Newton formula. The integrated method leads to the establishment of new delay-dependent sufficient conditions in form of linear matrix inequalities for asymptotic stability of delayed neural networks (DNNs). A numerical simulation study is conducted to demonstrate the obtained theoretical results, which shows their less conservatism than the existing stability criteria.

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