Stability Analysis for a Class of Stochastic Differential Equations with Impulses

This paper is concerned with the problem of asymptotic stability for a class of stochastic differential equations with impulsive effects. A sufficient criterion on asymptotic stability is derived for such impulsive stochastic differential equations via Lyapunov stability theory, bounded difference condition and martingale convergence theorem. The results show that the impulses can facilitate the stability of the stochastic differential equations when the original system is not stable. Finally, the feasibility of our results is confirmed by two numerical examples and their simulations.

Automated summary

This paper studies the asymptotic stability problem for a class of stochastic differential equations with impulsive effects. We derive a sufficient criterion on asymptotic stability using Lyapunov stability theory, bounded difference condition and martingale convergence theorem. The results indicate that impulses can enhance the stability of the stochastic differential equations when the original system is unstable. Finally, we validate the feasibility of our results through two numerical examples and simulations.