Almost sure exponential stability and stochastic stabilization of stochastic differential systems with impulsive effects

This paper focuses on the problem of almost sure exponential stability and stochastic stabilization of nonlinear stochastic differential systems with impulsive effects. The moment stability analysis of impulsive stochastic differential systems has received considerable attention. But relatively little is known about the almost sure exponential stability and noise stabilization. In this paper, by using Lyapunov function, we shall not only establish the general criteria on almost sure exponential stability for general nonlinear impulsive stochastic differential systems but also discuss exact method to design a stochastic perturbation to stabilize a given unstable impulsive differential systems. The efficiency of the proposed results is illustrated by a numerical example.