Global synchronization of complex networks with discrete time delays and stochastic disturbances

Abstract

This paper regards the global synchronization problem for a class of complex networks with both discrete time delays and stochastic disturbances. A sufficient condition that ensures the complex system to be globally synchronized is derived by referring to the Lyapunov functional method and the properties of Kronecker product. By using ‘delay-fractioning’ approach, the upper bounds of time delays of complex networks are greatly enlarged when synchronization achieves. Therefore, the result obtained in this paper is much less conservative than the existing ones. Furthermore, the proposed synchronization criterion, which is expressed in terms of linear matrix inequalities (LMIs), can be efficiently solved employing the Matlab LMI toolbox.