Stability of Solutions for Stochastic Impulsive Systems via Comparison Approach

This note studies stability problem of solutions for stochastic impulsive systems. By employing Lyapunov-like function method and It´s formula, comparison principles of existence and uniqueness and stability of solutions for stochastic impulsive systems are established. Based on these comparison principles, the stability properties of stochastic impulsive systems are derived by the corresponding stability properties of a deterministic impulsive system. As the application, the stability results are used to design impulsive control for the stabilization of unstable stochastic systems. Finally, one example is given to illustrate the obtained results.