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Title: Exponential synchronization of complex networks with Markovian jump and mixed delays
Authors: Liu, Y
Wang, Z
Liu, X
Keywords: Synchronization;Complex network;Markovian Jumping;Discrete time-delay;Distributed time-delay;Kronecker product;Linear matrix inequality
Issue Date: 2008
Publisher: Elsevier
Citation: Physics Letters A, 372(22): 3986-3998, May 2008
Abstract: 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.
Description: This is the post print version of the article. The official published version can be obtained from the link - Copyright 2008 Elsevier Ltd
ISSN: 0375-9601
Appears in Collections:Computer Science
Dept of Computer Science Research Papers

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