Stability of multi-link delayed impulsive stochastic complex networks with Markovian switching

Abstract

This article presents an analysis of p-th moment exponential stability for a class of stochastic functional differential systems with Markovian switching on complex multi-link networks using multi-delayed impulsive control. The multi-delayed impulsive control scheme implies that the impulsive jumps are related to multiple past states of the systems, which increases the complexity of the analysis. Additionally, single-link networks are extended to complex multi-link networks, which are more extensive. By combining graph theory and the Razumikhin method, several criteria for achieving p-th moment exponential stability for systems are derived. The criteria are related to the maximum upper bound of delays, impulsive interval, and network topology. Subsequently, the stability of multi-link stochastic complex networks with time delays and Markovian switching is studied using delayed impulsive control. Finally, the exponential stability of a class of stochastic coupled multi-link oscillators with Markovian switching is analyzed, and several numerical simulations are provided to verify the validity of the theoretical results.