LMI optimization approach to synchronization of stochastic delayed discrete-time complex networks

Complex networks are widespread in real-world systems of engineering, physics, biology, and sociology. This paper is concerned with the problem of synchronization for stochastic discrete-time drive-response networks. A dynamic feedback controller has been proposed to achieve the goal of the paper. Then, based on the Lyapunov second method and LMI (linear matrix inequality) optimization approach, a delay-independent stability criterion is established that guarantees the asymptotical mean-square synchronization of two identical delayed networks with stochastic disturbances. The criterion is expressed in terms of LMIs, which can be easily solved by various convex optimization algorithms. Finally, two numerical examples are given to illustrate the proposed method.