A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances

In this Letter, the synchronization problem is investigated for a class of stochastic complex networks with time delays. By utilizing a new Lyapunov functional form based on the idea of 'delay fractioning', we employ the stochastic analysis techniques and the properties of Kronecker product to establish delay-dependent synchronization criteria that guarantee the globally asymptotically mean-square synchronization of the addressed delayed networks with stochastic disturbances. These sufficient conditions, which are formulated in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. The main results are proved to be much less conservative and the conservatism could be reduced further as the number of delay fractioning gets bigger. A simulation example is exploited to demonstrate the advantage and applicability of the proposed result.