Exponential Stability of Stochastic Nonlinear Delay Systems Subject to Multiple Periodic Impulses

This article is devoted to stability analysis of stochastic nonlinear delay systems subject to multiple periodic impulses. By means of the stochastic analysis technique and improved Razumikhin method, we obtain several novel stability criteria under the combined action of impulsive disturbance and impulsive control. It is worth noting that the definition of globally weakly stochastically exponential stability is introduced and this article is the first attempt to study such stability notion for the considered system. In particular, we further discuss the double effects brought by multiple periodic impulses. As a verification, two numerical examples are presented to show the validity of the obtained results both theoretically and practically.