Asymptotical Synchronization of Coupled Nonlinear Partial Differential Systems With Impulsive Effects

This paper considers the asymptotical synchronization of coupled nonlinear impulsive partial differential systems (PDSs) in complex networks. The cases of both complex networks with fixed topology and switching topology are studied. Based on the Lyapunov–Krasoviskii functional method, sufficient conditions are presented to guarantee the asymptotical synchronization of nonlinear impulsive PDSs, under the cases of fixed topology or switching topology. The effect of the spatial domain is exhibited in these sufficient conditions. Moreover, these sufficient conditions provide a method for selecting a suitable impulsive strategy for the coupled PDSs to achieve the asymptotical synchronization. Finally, numerical examples are given to illustrate the correctness.     

Stochastic synchronization of delayed multiagent networks with intermittent communications: An impulsive framework

This paper investigates the stochastic synchronization problem of delayed multiagent networks with intermittent communications. Two kinds of impulsive effects are taken into account, ie, impulsive controller (positive impulsive effect) and impulsive disturbance (negative impulsive effect). Impulsive controller allows the synchronization to be realized and requires only state information exchange at discrete time instants such that the communication cost of bandwidth is reduced. Meanwhile, impulsive disturbance is inevitable in most of practical systems and therefore is taken into consideration at discrete time instants. Sufficient conditions for synchronization are given in terms of the graph topology, the control coupling gains, and the individual agent dynamics parameters, which indicates that synchronization can be realized if the impulsive effects coefficients and communication rate are suitably selected. Simulation results verify the effectiveness of the proposed synchronization protocol.     

Synchronization of complex switched delay dynamical networks with simultaneously diagonalizable coupling matrices

This paper studies local exponential synchronization of complex delayed networks with switching topology via switched system stability theory. First, by a common unitary matrix, the problem of synchronization is transformed into the stability analysis of some linear switched delay systems. Then, when all subnetworks are synchronizable, a delay-dependent sufficient condition is given in terms of linear matrix inequalities （LMIs） which guarantees the solvability of the synchronization problem under an average dwell time scheme. We extend this result to the case that not all subnetworks are synchronizable. It is shown that in addition to average dwell time, if the ratio of the total activation time of synchronizable and non-synchronizable subnetworks satisfy an extra condition, then the problem is also solvable. Two numerical examples of delayed dynamical networks with switching topology are given, which demonstrate the effectiveness of obtained results.     

Geometrical Dissipativity‐Based Output Synchronization of Discrete Dynamical Networks with Non‐Identical Nodes

In this paper, we investigate the generalized output synchronization problem for discrete dynamic networks with non‐identical nodes. We consider two cases: output synchronization for fixed topology and arbitrary switching topology. For the first case, we establish several criteria for generalized output synchronization using the geometrical dissipativity property. For the other case, we present a LaSalle invariance principle for discrete switched systems, based on which criteria for generalized output synchronization under arbitrary switching topology are given. Finally, an example is provided to illustrate the effectiveness of the main results.     

Consensus of multi-agent linear dynamic systems via impulsive control protocols

In this article, we introduce impulsive control protocols for multi-agent linear dynamic systems. First, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the consensus of the multi-agent linear dynamic systems by the theory of impulsive systems. Furthermore, how to select the discrete instants and impulsive matrices is discussed. The case that the topologies of networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.     

Impulsive consensus seeking in directed networks of multi-agent systems with communication time delays

In this article, we consider average consensus problem in directed delayed networked multi-agent systems having impulsive effects with fixed topology and stochastic switching topology. A simple impulsive consensus protocol for such networks is proposed, and some generic criteria for solving the average consensus problem are analytically derived. It is shown that a directed delayed networked multi-agent system can achieve average consensus globally exponentially with suitable impulsive gain and impulsive interval. Subsequently, two typical illustrative examples, along with computer simulation results, are provided to visualise the effectiveness and feasibility of our theoretical results.     

具有切换拓扑结构的非恒等节点复杂网络同步化判据

网络拓扑结构与节点动态在复杂网络的同步化过程中起着关键性的作用,针对具有切换拓扑结构与非恒等节点的同步化问题还没有非常有效的判据.本文研究了具有切换拓扑与非恒等节点的复杂网络同步化问题,针对非恒等节点不存在公共平衡解的情况,选取所有节点的平均状态作为同步化目标,并在此基础上建立起误差动态方程.基于所有外部耦合矩阵可以同时三角化的条件下,构建了低维系统的公共Lyapunov函数,提出了在误差向量范数有界意义下的复杂网络全局同步化判据,保证系统在任意切换策略下实现复杂网络的同步化.最后通过数值仿真验证了结果的有效性.     

Exponential synchronization of impulsive complex networks with output coupling

This paper proposes a new impulsive complex delayed dynamical network model with output coupling, which is totally different from some existing network models. Then, by employing impulsive delay differential inequalities, some sufficient conditions are obtained to guarantee the global exponential state synchronization and output synchronization of the impulsive complex delayed dynamical network. Finally, two numerical examples are given to demonstrate the effectiveness of the obtained results.     

Stability analysis and H∞ control for hybrid complex dynamical networks with coupling delays

This paper formulates and studies a model of complex dynamical networks with switching topology and coupling delays. Based on the hybrid control and Lyapunov function, the stability and robust H_∞ control of such networks with impulsive and switching effects, which have not been studied before, are addressed with some criteria derived. Examples are given to illustrate the effectiveness of the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

Synchronization of complex dynamical networks with switching topology: A switched system point of view

In this paper, we study the synchronization problem for complex dynamical networks with switching topology from a switched system point of view. The synchronization problem is transformed into the stability problem for time-varying switched systems. We address two basic problems: synchronization under arbitrary switching topology, and synchronization via design of switching within a pre-given collection of topologies when synchronization cannot be achieved by using any topology alone in this collection. For the both problems, we first establish synchronization criteria for general connection topology. Then, under the condition of simultaneous triangularization of the connection matrices, a common Lyapunov function (for the first problem) and a single Lyapunov and multiple Lyapunov functions (for the second problem) are systematically constructed respectively by those of several lower-dimensional dynamic systems. In order to achieve synchronization using multiple Lyapunov functions, a stability condition and switching law design method for time-varying switched systems are also presented, which avoid the usual non-increasing condition.     

具有脉冲耦合复杂时滞动力网络的同步

考虑了一个具有脉冲耦合的复杂时滞动力网络的同步问题.基于脉冲时滞动力系统扩展的Halanay不等式,给出了网络同步的一个充分条件.所获结果表明,即使网络节点之间仅在一些离散时刻存在瞬时连接,网络仍然能够达到同步.进一步将所得结果应用于一个由混沌FHN神经元振子为动力节点所构成的一个无标度的动力网络,数值仿真结果表明了理...     

具有拓扑切换特性的离散型不确定时空网络的指数同步

研究了具有拓扑切换特性的离散型不确定时空网络的指数同步问题. 基于稳定性理论, 构造了具有指数形式的Lyapunov函数, 并设计了同步控制器的结构方程, 进而获得了时空网络的同步条件. 同时, 我们设计了未知参数的识别律, 有效地识别了网络中的未知参数. 最后, 选取实际的激光相位共轭波空间扩展系统作为网络节点进行仿真模拟, 验证了同步方案的可行性与控制器的有效性. 通过构造具有指数形式的Lyapunov函数, 能够有效地调节网络的同步速率. 并且获得的同步条件中不包含网络的耦合矩阵项, 消除了拓扑切换特性对同步过程的影响, 使得网络同步性能更加稳定.     

Adaptive synchronization of uncertain coupled stochastic complex networks

In this paper, the problem of adaptive synchronization of uncertain coupled complex networks is investigated. Some controllers and adaptive laws are designed to ensure achieving synchronization of a general complex network model. In particular, synchronization of coupled stochastic networks subject to random perturbations is studied, with a referenced node introduced as the target node for synchronization. An example is simulated on delayed neural networks coupled in a small‐world network topology, which demonstrates the feasibility and effectiveness of the proposed adaptive control method. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Leader–follower synchronization of networked multi-agent systems via hybrid protocols

This paper studies the leader–follower synchronization problem of complex-valued networked multi-agent systems with time-delay. A new hybrid protocol including a continuous-time protocol which is based on the interaction topology of follower agents and a pinning delayed impulsive control protocol is proposed. By employing the Lyapunov functional method in complex domains and the mathematical analysis technique, several delay-dependent leader–follower synchronization criteria are established that take into account various sizes of delays. Particularly, our result shows that leader–follower synchronization of delayed complex-valued networked multi-agent systems can be achieved even if the proposed hybrid protocol is being subject to relatively large impulse delays. A numerical example is provided to illustrate the effectiveness of the theoretical results.     

Impulsive Control and Synchronization for Delayed Neural Networks With Reaction–Diffusion Terms

This paper discuss the global exponential stability and synchronization of the delayed reaction–diffusion neural networks with Dirichlet boundary conditions under the impulsive control in terms of $p$-norm and point out the fact that there is no constant equilibrium point other than the origin for the reaction–diffusion neural networks with Dirichlet boundary conditions. Some new and useful conditions dependent on the diffusion coefficients are obtained to guarantee the global exponential stability and synchronization of the addressed neural networks under the impulsive controllers we assumed. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed control methods.      

Global exponential synchronization of stochastic switching networks with time‐varying delay

This paper is concerned with the global exponential synchronization of stochastic delayed switching networks via hybrid control. The network under investigation is quite general to reflect the reality, where the network topology consists of r modes and switches from one mode to another according to a Markovian chain with known transition probability. Parameter uncertainties, time varying delay and stochastic disturbances are all taken into account in this study. Based on the Lyapunov functional method and stochastic analysis techniques, some new criteria for the global robust synchronization via hybrid control are established. Finally, one example with numerical simulation is given for illustration. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

离散混沌网络系统中共同噪声诱导同步的条件

噪声普遍存在于各种真实系统和人造系统中,它对系统的同步动力学具有多重影响.本文探索外部噪声对高维离散复杂网络系统同步行为的积极作用.首先构建外部共同噪声驱动下两个参数相同、未耦合的离散混沌网络模型,然后利用Birkhoff遍历定理与矩阵论等相关理论,严格证明了噪声诱导两个离散混沌网络系统取得同步的充分条件,进一步借助于具体的混沌网络模型,利用数值仿真验证了理论分析的有效性.数值模拟的结果表明当网络模型参数满足理论分析的充分条件时,共同噪声可以诱导两个参数相同、未耦合的离散混沌网络在随机意义下取得同步,而且同步效果不依赖于复杂网络拓扑结构的选取.     

Exponential Lagrange stability for impulses in discrete-time delayed recurrent neural networks

This paper focuses on the problem of exponential stability in the sense of Lagrange for impulses in discrete-time delayed recurrent neural networks. By establishing a delayed impulsive discrete inequality and a novel difference inequality, combining with inequality techniques, some novel sufficient conditions are obtained to ensure exponential Lagrange stability for impulses in discrete-time delayed recurrent neural networks. Meanwhile, exponentially convergent scope of neural network is given. Finally, several numerical simulations are given to demonstrate the effectiveness of our results.     

复杂网络的脉冲同步

研究了具有有界耦合函数的不确定复杂动态网络的脉冲同步问题．根据脉冲控制的概念和脉冲微分方程的稳定性理论,我们利用一个灵活有效的脉冲控制实现了复杂动态网络的脉冲同步．最后,通过对混沌系统做网络节点的动态网络的数字模拟,验证了我们提出的脉冲控制方案的有效性和实用性．     

On the exponential synchronization of stochastic impulsive chaotic delayed neural networks

In this paper, the exponential synchronization of stochastic impulsive chaotic delayed neural networks is investigated. Based on the Lyapunov function method, time-varying delay feedback control technique and the efficient modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical chaotic delayed neural networks with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities (LMIs), which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Comparing with the existing works that consider single perturbation (stochastic or impulsive one), the proposed method can provide a more general framework for the synchronization of multi-perturbation chaotic systems, which is favorable for practical application in secure communication. Finally, numerical simulations verify the effectiveness of the proposed method.