Stability of stochastic nonlinear delay systems with delayed impulses

Abstract

In this paper, we study the input-to-state stability of a class of stochastic delay differential equations with delay impulses. We consider the two cases where the continuous stochastic delay system is stable and unstable, and establish different types of stability conditions by using the average dwell time and the vector Lyapunov function method. Finally, two examples are used to verify the validity of our results.