Exponential synchronization of complex networks with Markovian jump and mixed delays

作     者：Liu, Yurong Wang, Zidong Liu, Xiaohui 

作者机构：Yangzhou Univ Dept Math Yangzhou 225002 Peoples R China Brunel Univ Dept Informat Syst & Comp Uxbridge UB8 3PH Middx England 

出 版 物：《PHYSICS LETTERS A》 (Phys Lett Sect A Gen At Solid State Phys)

年 卷 期：2008年第372卷第22期

页      面：3986-3998页

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

基　　金：Biotechnology and Biological Sciences Research Council, BBSRC, (100/EGM17735, BB/C506264/1) Alexander von Humboldt-Stiftung Natural Science Foundation of Jiangsu Province, (BK2007075) National Natural Science Foundation of China, NSFC, (60774073) Engineering and Physical Sciences Research Council, EPSRC, (GR/S27658/01, EP/C524586/1) Royal Society 

主　　题：synchronization complex network Markovian jumping discrete time-delay distributed time-delay Kronecker product linear matrix inequality 

摘      要：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.