Stability Analysis On Solutions Of Several Impulsive Stochastic Functional Differential Systems

In the real world, there always exist stochastic perturbations and impulse phe-nomena.In order to more accurately describe the systems, and precisely reveal their variation, it is necessary to consider the influence of stochastic perturbations and im-pulse phenomena to the system. This dissertation is mainly concerned with the sta-bilization of solutions for several classes of impulsive stochastic functional differential systems and summarized as follows.In Chapter 1, the research background, significance and status are reviewed, and the main work is outlined.The chapter 2 is concerned with the stabilization of two classes of impulsive s-tochastic differential systems. By virtue of comparison theorem of stochastic equations and Ito formula, the stability of solutions of two impulsive stochastic differential sys-tems is obtained respectively, whose impulse is the sum of a linear function and a nolinear function, and the other impulse is a variable linear function.The stabilization of stochastic differential equations with delay impulse is discussed in the chapter 3. Based on the Razumikhin technique and method of Lyapunov func-tions, several criteria on p-th moment stability and p-th moment asymptotic stability are established, which improve the existing correlation results.In the last chapter, the decay stability for solutions of stochastic functional dif-ferential systems with impulse is investigated. By using Razumikhin techniques, Lya-punov functions method, B-D-G inequality and Holder inequality, p-th moment decay stability and almost sure decay stability are obtained, which are more general than the existing correlation results.