The P-th moment asymptotic stability of stochastic system with variable-time impulses

In this paper, we explore some aspect of the asymptotic stability of stochastic impulsive systems with variable-time impulses. At the beginning we consider the case that the trajectory of the stochastic system intersects each surface exactly once. Then we shall show that under the well-selected conditions the systems with variable-time impulsive can be changed to the systems with the fixed-time impulsive. Some criteria ensuring the stability in the p-th moment are obtained by using stochastic analysis theory. An illustrative example and simulations are given to show the effectiveness of our results.