Impulsive control for synchronizing delayed discrete complex networks with switching topology

In this paper, global exponential synchronization of a class of discrete delayed complex networks with switching topology has been investigated by using Lyapunov-Ruzimiki method. The impulsive scheme is designed to work at the time instant of switching occurrence. A time-varying delay-dependent criterion for impulsive synchronization is given to ensure the delayed discrete complex networks switching topology tending to a synchronous state. Furthermore, a numerical simulation is given to illustrate the effectiveness of main results     

Robust Stabilization of Uncertain Networked Control Systems with Data Packet Dropouts

The data packet dropouts phenomenon is usually inevitable when information transmit- ted among communication networks.In this paper,the robust stabilization problem for uncertain networked control systems with data packet dropouts is studied.First,an uncertain discrete-time switching system model is presented to describe these networked control systems.The stability equiv- alence is then proved between this switching system and an uncertain impulsive difference system. Moreover,a sufficient condition is obtained for the asymptotical stability of the nonlinear impulsive difference system.From this condition the robust stabilization problem is dealt with for the uncertain impulsive system.Main results are given in linear matrix inequalities.Finally a numerical example is given to illustrate the theoretical results.     

不确定有损网络控制系统的鲁棒镇定

The data packet dropouts phenomenon is usually inevitable when information transmitted among communication networks. In this paper, the robust stabilization problem for uncertain networked control systems with data packet dropouts is studied. First, an uncertain discrete-time switching system model is presented to describe these networked control systems. The stability equivalence is then proved between this switching system and an uncertain impulsive difference system. Moreover, a sufficient condition is obtained for the asymptotical stability of the nonlinear impulsive difference system. From this condition the robust stabilization problem is dealt with for the uncertain impulsive system. Main results are given in linear matrix inequalities. Finally a numerical example is given to illustrate the theoretical results.     

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.     

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.     

Multi-weighted Complex Structure on Fractional Order Coupled Neural Networks with Linear Coupling Delay: A Robust Synchronization Problem

This sequel is concerned with the analysis of robust synchronization for a multi-weighted complex structure on fractional-order coupled neural networks (MWCFCNNs) with linear coupling delays via state feedback controller. Firstly, by means of fractional order comparison principle, suitable Lyapunov method, Kronecker product technique, some famous inequality techniques about fractional order calculus and the basis of interval parameter method, two improved robust asymptotical synchronization analysis, both algebraic method and LMI method, respectively are established via state feedback controller. Secondly, when the parameter uncertainties are ignored, several synchronization criterion are also given to ensure the global asymptotical synchronization of considered MWCFCNNs. Moreover, two type of special cases for global asymptotical synchronization MWCFCNNs with and without linear coupling delays, respectively are investigated. Ultimately, the accuracy and feasibility of obtained synchronization criteria are supported by the given two numerical computer simulations.

     

Exponential synchronization of coupled memristive neural networks with time delays

In this paper, the model of coupled memristive neural networks with time delays is established, and sufficient conditions are obtained that guarantee the exponential synchronization for such system. Memristive network exhibits state-dependent switching behaviors due to the physical properties of memristor. It is demonstrated that the synchronization performance is largely dependent on the coupling pattern and strength among memristive neural networks. Moreover, the information exchange graph of the underlying network topology need not be undirected or strongly connected. Finally, numerical simulations are given to verify the usefulness and effectiveness of our results.     

Consensus of multi-agent systems based on sampled-data control

This article studies the consensus problem in directed networks, assuming that each agent is with double-integrator dynamics and only obtains the measurements of its positions relative to its neighbours at sampling instants. We propose a protocol based on sampled-data control and derive an equivalent characterisation of the solvability of the consensus problem under this protocol. In virtue of this equivalent characterisation, we further consider two cases: fixed topology and switching topology. For the first case, we present a set of sampling periods and feedback coefficients which ensure that the protocol can solve a consensus problem. For the second case, we derive sufficient conditions for the protocol to solve a consensus problem under arbitrary switching signals and under a class of switching signals, respectively. Finally, simulations are provided to illustrate the effectiveness of the theoretical results.     

Master‐slave synchronization for coupled neural networks with Markovian switching topologies and stochastic perturbation

In this paper, the master‐slave synchronization for coupled neural networks with Markovian jumping topology and stochastic perturbation is discussed. Based on a graph theory, the ergodic property of the Markovian chain, and the strong law of the large numbers for local martingales, several sufficient conditions are established to ensure the almost sure exponential synchronization or asymptotic synchronization in mean square for coupled neural networks with Markovian jumping topology. By the pinning control method, the chaotic synchronization between the master system and the slave systems with stochastic disturbance is achieved. The effectiveness of the results is finally illustrated by a numerical example.     

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.     

噪声下相互依存网络的自适应H∞异质同步

针对具有噪声的相互依存复杂动力网络, 本文研究了它的局部自适应H_∞异质同步问题.该网络由两个具有"一对一"相互依赖关系的子网构成, 子网内部耦合和子网间的耦合均含有未知但有界的非线性函数.基于李雅普诺夫稳定性理论、线性矩阵不等式(Linear matrix inequality, LMI)技术和自适应以及H_∞控制方法, 本文提出了使得相互依存网络在外部噪声的干扰下, 两个子网各自达到一致的充分条件.这些条件不仅可以保证受扰动的网络获得鲁棒渐近同步而且可以让网络达到一个给定的鲁棒H_∞水平.最后的数值模拟验证了提出的方法的有效性以及可行性.     

Global exponential synchronization for coupled switched delayed recurrent neural networks with stochastic perturbation and impulsive effects

This paper focuses on the hybrid effects of stochastic perturbation, system switching, state delays and impulses on neural networks. Based on the Lyapunov functional method, switching analysis techniques, the comparison principle and a new impulsive delay differential inequality, we derive some sufficient conditions which depend on delay and impulses to guarantee the exponential synchronization of the coupling delay switching recurrent neural networks with stochastic perturbation. Simulation results finally demonstrate the effectiveness of the theoretical results.     

Consensus seeking of high-order dynamic multi-agent systems with fixed and switching topologies

This article studies a consensus problem for a group of high-order dynamic agents with fixed and switching topologies. Two linear consensus protocols, which only depend on the agent's own information and its neighbours' partial information, are proposed, respectively, for the group with and without communication time-delays. For the case of fixed topology and zero communication time-delay, a necessary and sufficient condition for the consensus is established. The parameter design of the protocol is also discussed. Under switching topology, the consensus is investigated for two cases: the case of zero communication time-delay and the case of nonuniform communication time-delays. For each case, a sufficient condition for the consensus is provided. Moreover, for a group of double/triple-integrator agents with fixed topology and uniform constant time-delay, some necessary and sufficient conditions for the consensus are given. Finally, numerical simulations are worked out to illustrate the effectiveness of the theoretical results.     

Distributed impulsive synchronization of Lur'e dynamical networks via parameter variation methods

This paper is devoted to investigating the exponential synchronization of coupled Lur'e dynamical networks with multiple time‐varying delays and stochastic disturbance. The problem studied in this paper could be regarded as a kind of leader‐following synchronization issue. As the networks may suffer from certain impulsive disturbance, an effective distributed impulsive control protocol is proposed to synchronize the stochastic Lur'e dynamical networks. According to the comparison principle, the average impulsive interval, and the extended formula for the variation of parameters, sufficient conditions are derived for successful achievement of the network synchronization with consideration to different functions of impulsive effects. Furthermore, the exponential convergence rate is obtained based on the impulsive solution equation. In addition, finally, some numerical simulations are given to illustrate the validity of the control scheme and the theoretical analysis.     

脉冲Hopfield神经网络的鲁棒H-稳定性及其脉冲控制器设计

研究了脉冲Hopfield神经网络在Hopfield意义下的鲁棒稳定性. 通过应用Lyapunov函数法和Riccati不等式方法, 得到了脉冲Hopfield神经网络鲁棒稳定和鲁棒渐近稳定的充分条件, 在此基础上, 设计出了易于实施的脉冲控制器来镇定Hopfield神经网络. 最后, 给出了例子.     

Distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies

In this article, we study distributed consensus of heterogeneous multi-agent systems with fixed and switching topologies. The analysis is based on graph theory and nonnegative matrix theory. We propose two kinds of consensus protocols based on the consensus protocol of first-order and second-order multi-agent systems. Some necessary and sufficient conditions that the heterogeneous multi-agent system solves the consensus problems under different consensus protocols are presented with fixed topology. We also give some sufficient conditions for consensus of the heterogeneous multi-agent system with switching topology. Simulation examples are provided to demonstrate the effectiveness of the theoretical results.     

离散多智能体切换系统的二阶分组一致性研究

针对随机切换拓扑下离散多智能体系统的二阶分组一致性问题进行了研究。 设计了一种新颖的分组一致性协议,该协议不依赖于保守的假设条件,能全面反映系统中智能体在分组内与分组间的相互影响。引入马尔科夫链来模拟系统的随机拓扑变化, 基于矩阵理论和图论得到了在马尔科夫切换拓扑条件下,应用新协议使系统达到分组一致的充分条件。 在证明过程的结尾部分,使用线性不等式 (LMI) 工具给出了获取协议中控制参数的算法。最后,通过数字仿真实例证明了理论结果的有效性。     

Stabilisability of discrete-time multi-agent systems under fixed and switching topologies

This paper studies the problem of stabilisability for general discrete-time linear multi-agent systems. For fixed topology, a necessary and sufficient graph-theoretic condition is proposed. Based on this, a general linear form of the external control input is given, and two methods to design the feedback gain matrix by Riccati equality/inequality are given. For switching topology, a sufficient graph-theoretic condition is presented, under which the stabilisability of multi-agent systems is achieved by introducing an averaging analysis approach. Additionally, both results under fixed and switching topologies are applied for solving the tracking and formation control of discrete-time multi-agent systems, and some sufficient and/or necessary conditions are presented. Finally, numerical examples are given to illustrate the theoretical results.     

Exponential synchronization of nonlinear multi‐agent systems with time delays and impulsive disturbances

The problem of cooperative synchronization of nonlinear multi‐agent systems with time delays is investigated in this paper. Compared with the existing works about synchronization (or consensus) of multi‐agent systems, the method in this paper provides a more general framework by considering nonlinear multi‐agent systems with time delays and impulsive disturbances. The model in this paper is sufficiently general to include a class of delayed chaotic systems. Based on the Lyapunov stability theory and algebraic graph theory, sufficient conditions are presented to guarantee the cooperative exponential synchronization for these multi‐agent delayed nonlinear systems. These conditions are expressed in terms of linear matrix inequalities, which can easily be checked by existing software tools. It is seen that the Lyapunov functions must be constructed based on the graph topology to prove synchronization. The well‐known master–slave (drive‐response) synchronization of two chaotic delayed systems is a special case of this paper, and therefore, the results in this paper are also useful for practical applications in secure communication. Simulation results verify the effectiveness of the proposed synchronization control algorithm. Copyright © 2015 John Wiley & Sons, Ltd.