Stability Analysis Of Some Classes Of Stochastic Differential Systems Via The Vector Lyapunov Function Method

Stochastic differential systems have been widely studied because stochastic modeling plays an important role in many branches of science and engineering,especially in the application of control theory.In the control system theory,the stability of the system is the most basic and important concept.Therefore,stability analysis is a hot topic in the study of stochastic differential systems.Lyapunov function method is widely used in the study of the stability of stochastic differential systems,and most of the stability theorems in the literature are based on scalar Lyapunov function.In recent years,more and more attention has been paid to stability analysis based on vector Lyapunov function method.In this paper,we use the vector Lyapunov function to analyze the stability of several kinds of stochastic differential systems.The main results of this paper can be summarized as follows:Firstly,we study the th moment exponential stability and the almost sure exponential stability of neutral stochastic delay differential systems.In the case of removing the linear growth condition,we establish a L-operator differential inequality based on vector Lyapunov function with cross terms,and prove the existence and stability of global solution of neutral stochastic delay differential systems.Secondly,we study the th moment exponential stability of impulsive stochastic functional differential systems.Based on vector Lyapunov function,Razumikhin-type technique and average dwell-time method,we establish a vector Razumikhin-type stability theorem for impulsive stochastic functional differential systems.Thirdly,based on the vector Lyapunov function method and average dwell-time method,we study the stochastically input-to-state type stability and the th moment exponential stability of stochastic delay differential systems with delayed impulses.