Stability Analysis Of Some Classes Of Impulsive Stochastic Differential Systems

Impulsive stochastic differential equations have attracted extensive attention from domestic and foreign scholars because they can be used to simulate dynamic systems in which the states of the systems undergo instantaneous changes at certain moments.And the stability of the system i5 the premise of its normal operation,so stability analysis is a vital subject among the theoretical studies of stochastic differen-tial equations.In this paper,we investigate sufficient conditions for the stabilities of some classes of impulsive stochastic systems.The main results of this paper can be summarized as the following three parts.Firstly,we study the pth moment globally asymptotic stability in probability and pth stochastic input-to-state stability of impulsive stochastic systems with Markovian switching.By means of the average dwell time condition,we obtain some novel suffi-cient conditions to ensure these stability properties.In particular,the coefficient of the Lyapunov function is extended to be time-varying.Furthermore,the nonlinear restric-tions on drift and diffusion coefficients are put to substitute some previous conditions,which improve the existing linear results.Secondly,we discuss the input-to-state type stability and exponential stability of the stochastic functional differential systems with delayed impulses.In order to solve the difficulties caused by delayed impulses,we propose a generalized comparison principle and study the property of the solution of an impulsive differential equation.By applying the average impulsive interval approach,the stability properties of the system are obtained.In particular,the coefficients of the upper bound for the diffu-sion operator of Lyapunov functions are allowed to be time-varying in both delay-free and delayed parts.Finally,the stabilities of a class of linear stochastic time-delay system under delayed impulsive control are investigated.The existing deterministic system is ex-tended to a stochastic system with discrete and distributed delays in both drift and diffusion terms.By applying the existing impulsive differential inequality,uniform stability,uniform asymptotic stability and exponential stability of the stochastic time-delay system are discussed,and a numerieal example is given to verify the validity of the results.