Stability of stochastic functional differential equations with impulses by an average approach

Abstract This paper is concerned with the stability issues of stochastic functional differential equations with impulsive effects. Several unified Lyapunov-type stability criteria are established based on the formula of the variation of parameters and the comparison principle of the impulsive systems. The sufficient conditions proposed in this paper depend mainly on the integral average value of the time-varying coefficients and the average impulsive interval, which are less conservative than previous literature. Two examples are provided to demonstrate the effectiveness of the theoretical results.