A delay fractioning approach to global synchronization of complex networks with distributed delays and stochastic disturbances

Abstract

In this paper, the global synchronization problem is studied for a class of complex networks. This is the first time that both the distributed delays and the stochastic disturbances are considered at the same time. Based on the idea of 'delay fractioning', a sufficient condition which ensures the complex system to be globally synchronized is derived by referring to the Lyapunov functional method and the properties of Kronecker product. The condition, which is expressed in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. The result obtained in this paper is proved to be much less conservative due to the fact that the delay upper bound is greatly enlarged. © 2009 Springer Berlin Heidelberg.