Delay-Dependent Impulsive Distributed Synchronization of Stochastic Complex Dynamical Networks With Time-Varying Delays

This paper studies the problem of synchronization for a class of stochastic complex dynamical networks. It designs for the first time a distributed impulsive protocol based on pinning control that involves a constant signal transmission delay to tackle synchronization issues of such networks. Novel criteria on network synchronization are established by employing a time-dependent Lyapunov functional and a mathematical induction approach, where information on the state variables themselves and their neighbors is sufficiently utilized. Moreover, it is shown that the frequency of impulsive occurrence, impulsive input delays, stochastic perturbations, and the feedback control strength can significantly affect the synchronization performance. Numerical simulations are given to illustrate the effectiveness of the derived theoretical results.