Exponential synchronization of complex networks with Markovian jump and mixed delays
Exponential synchronization of complex networks with Markovian jump and mixed delays
复制标题
具有马尔可夫跳跃和混合延迟的复杂网络的指数同步
DOI：
10.1016/j.physleta.2008.02.085
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发表时间：
2008-05-26
影响因子：
2.6
通讯作者：
Liu, Xiaohui
中科院分区：
文献类型：
--
作者：
Liu, Yurong;Wang, Zidong;Liu, Xiaohui
本文研究了一类具有马尔可夫跳跃和混合时滞的N个线性耦合复杂网络的指数同步问题。复杂网络由m个模式组成，网络按照已知转移概率的马尔可夫链从一个模式切换到另一个模式。混合时滞由离散时滞和分布时滞组成，这两种时滞都是模式相关的。假定复杂网络中的非线性项满足比常用的Lipschitz条件更一般的扇形条件。利用Kronecker乘积和随机分析工具，我们提出了一种新的适用于处理分布时滞的Lyapunov-Krasovskii泛函，并证明了当一组线性矩阵不等式(LMI)可行时，所解决的同步问题是可解的。为此，发展了一种统一的LMI方法来建立耦合复杂网络在均方意义下全局指数同步的充分条件。请注意，使用MatLab LMI工具箱可以很容易地求解LMI，并且不需要调整参数。最后给出了一个仿真实例，验证了所得主要结果的有效性。(C)2008年，爱思唯尔出版。
In this Letter, we investigate the exponential synchronization problem for an array of N linearly coupled complex networks with Markovian jump and mixed time-delays. The complex network consists of m modes and the network switches from one mode to another according to a Markovian chain with known transition probability. The mixed time-delays are composed of discrete and distributed delays, both of which are mode-dependent. The nonlinearities imbedded with the complex networks are assumed to satisfy the sector condition that is more general than the commonly used Lipschitz condition. By making use of the Kronecker product and the stochastic analysis tool, we propose a novel Lyapunov-Krasovskii functional suitable for handling distributed delays and then show that the addressed synchronization problem is solvable if a set of linear matrix inequalities (LMIs) are feasible. Therefore, a unified LMI approach is developed to establish sufficient conditions for the coupled complex network to be globally exponentially synchronized in the mean square. Note that the LMIs can be easily solved by using the Matlab LMI toolbox and no tuning of parameters is required. A simulation example is provided to demonstrate the usefulness of the main results obtained. (C) 2008 Published by Elsevier B.V.