Synchronization of stochastic dynamical networks under impulsive control with time delays.

In this paper, the stochastic synchronization problem is studied for a class of delayed dynamical networks under delayed impulsive control. Different from the existing results on the synchronization of dynamical networks under impulsive control, impulsive input delays are considered in our model. By assuming that the impulsive intervals belong to a certain interval and using the mathematical induction method, several conditions are derived to guarantee that complex networks are exponentially synchronized in mean square. The derived conditions reveal that the frequency of impulsive occurrence, impulsive input delays, and stochastic perturbations can heavily affect the synchronization performance. A control algorithm is then presented for synchronizing stochastic dynamical networks with delayed synchronizing impulses. Finally, two examples are given to demonstrate the effectiveness of the proposed approach.