Uniform stability of stochastic impulsive systems: A new comparison method

Abstract

This paper studies uniform stability problems of stochastic impulsive systems by using a new comparison method. We firstly establish a comparison principle between the stochastic impulsive system and its scalar comparison system. Based on the obtained comparison result, uniform stability and uniform asymptotic stability of stochastic impulsive systems are established by analyzing those of comparison systems. Finally, a numerical example of a power system with random perturbations is presented to illustrate our results.