Multi-delayed impulsive stability for stochastic multi-link complex networks with time-varying coupling structure

This article studied the exponential stability of stochastic functional differential systems based on directed networks, utilizing impulsive control with multiple delays. The impulsive control considered in this article is related to multi-past states since the impact of input delay for stability. It is worth mentioning that multi-link networks are constructed as extensions of single-link or double-link networks. The time-varying coupling strength is considered, which is generally but rarely considered in network stability. Several criteria, which are related to the network topology, input delays, and involved impulsive control schemes, are obtained based on Lyapunov-Razumikhin method and graph theory. Subsequently, the stability of multi-link stochastic time-varying networks with time delays is studied using delayed impulsive control. Finally, the theoretical results are applied to the oscillator system, and some numerical simulations are given.