Global Synchronization for Delayed Complex Networks with Randomly Occurred Nonlinearities and Multiple Stochastic Disturbances

This paper is concerned with the synchronization problem for a new class of continuous-time delayed complex networks with stochastic nonlinearities (randomly occurred nonlinearities), interval time-varying delays, unbounded distributed delays as well as multiple stochastic disturbances. The stochastic nonlinearities and multiple stochastic disturbances are investigated here in order to reflect more realistic dynamical behaviors of the complex networks that are affected by the noisy environment. By utilizing a new matrix functional with the idea of partitioning the lower bound ~1 of the time-varying delay, we employ the stochastic analysis techniques and the properties of Kronecker product to establish delay-dependent synchronization criteria that ensure the globally asymptotically mean-square synchronization of the addressed stochastic delayed complex networks. The sufficient conditions obtained are in form of linear matrix inequalities (LMIs) whose solution can be readily solved by using the standard numerical software. A numerical example is exploited to show the applicability of the proposed results.