Analysis Of The Stability Of Stochastic Implusive And Switched System

This article consists of two parts to study the stability of the stochastic impulsive and switched system.The first part studies the exponential stability of stochastic impulsive switched systems which consist of stable and unstable subsystems,the second part studies the almost surely exponential stability of nonlinear stochastic impulsive switched systems.For the first part,this paper studies the pth moment exponential stability of the linear impulsive switched stochastic systems with stochastic stable subsystems and stochastic unstable subsystems,systems with uncertainties are also studied.Then,the mean square exponential stability and robust of nonlinear stochastic impulsive switched systems with stochastic stable subsystems and stochastic unstable subsystems are studied.Using the Average Dwell Time method and piecewise Lyapunov function approach,some sufficient conditions of the pth exponential stability,the mean square exponential stability and the robust are obtained,that is when the total active time of stochastic stable subsystems compared to the total active time of stochastic unstable subsystems are more than a certain proportion.Finally some examples are given sto verify the theorems.The second part of this paper studies the almost surely exponential stability of nonlinear impulsive switched stochastic systems.Also using the Average Dwell Time method and piecewise Lyapunov function approach,through choosing a suitable switching law,we obtain the sufficient conditions of the almost surely exponential stability of the system.