Stability Analysis Of Stochastic Hybrid Systems With Delayed Impulses And Markovian Switching

On the one hand,much attention has been devoted to the stability of stochastic functional differential systems.If the Markovian switching is considered into the stochastic functional differential systems,the stochastic hybrid systems obtained in this way are more general.On the other hand,the impulsive effect may often affect the hybrid stochastic functional differential systems,and the problem of delayed impulses is common in practical systems.Therefore,it is very important to study the stability of hybrid stochastic functional differential systems with delayed impulses.Based on the Lyapunov function method,this dissertation investigates the stability of stochastic hybrid systems with delayed impulses and Markovian switching by using the stationary distribution of the Markov chain,the average impulsive interval,the formula of the variation of parameters and the comparison principle of impulsive systems.This dissertation mainly includes the following parts:The first chapter introduces the research background,significance and status of stochastic hybrid systems with delayed impulses and Markovian switching,and gives the preliminary knowledge.The second chapter studies the almost sure exponential stability of hybrid stochastic functional differential systems.Based on the stationary distribution of Markov chain,by constructing the appropriate Lyapunov function,the almost sure exponential stability of the corresponding hybrid stochastic differential systems is obtained firstly.And then on the basis of this conclusion,combined with the stability analysis method,a new theorem on almost sure exponential stability of the hybrid stochastic functional differential systems is established.In particular,the results are applicable to some systems which do not satisfy the properties of M-matrix.Finally,the results are applied to the stochastic stabilization problem based on discrete-time state observations.The third chapter investigates the stability of hybrid stochastic functional differential systems with delayed impulsive effects.Based on the Lyapunov function method,the sufficient conditions for pth moment asymptotic stability and pth moment exponential stability of the systems are obtained by using the average impulsive interval,the formula of variation of parameters,and combining with the comparison principle of the impulsive systems.Particularly,the results are related to time-varying coefficients and have wider application.Finally,an example is given to illustrate the effectiveness of the results.In the end,the whole dissertation is summarized and the further researches are proposed.