Exponential Stability And Impulsive Stabilization Of Hybrid Stochastic Differential Systems With Delayed Impulse

The doctoral dissertation intends to study the stability and impulsive stabilization of hybrid stochastic functional differential systems with delayed impulsive effects.Based on the average impulsive interval,Lyapunov function,Razuminkhin techniques and some stochastic analysis techniques,the stability and impulsive stabilization of stochastic functional differential systems with delayed impulsive effects are studied.The main contents and contribution of this dissertation are as follows:The first chapter,an introduction to the background and significance of hybrid impulsive stochastic differential system is given.Also,the previous achievements are presented.The second chapter,the exponential stability and impulsive stabilization of hybrid stochastic differential systems with delayed effects are studied.By employing average impulsive interval,Lyapunov function and linear matrix inequality approach,some pth moment exponential stability and impulsive stabilization criteria are established.Especially,the obtained results get rid of the restrictions on the supremum or infimum of impulsive interval,thus it is less conservative.Finally,two examples are discussed to illustrate the effectiveness and advantages.The third chapter,the exponential stability and delayed impulsive sta-bilization of hybrid stochastic differential systems are investigated.Based on Lyapunov function,Razuminkhin techniques and some stochastic analysis techniques,some pth moment exponential stability and impulsive stabilization criteria are obtained.Especially,the obtained results show that the delayed part of impulses can make contribution to the stability of the system.There-fore,our results have a wider rang.Finally,three examples are discussed to illustrate the effectiveness and advantages.The fourth chapter,the conclusions are summarised and the future studies are proposed.