Stability Study Of Stochastic Differential Systems With Mixed Impulses

Because the impulsive phenomenon is widespread in nature,the research of the impulse stochastic differential systems has been paid attention by many researcher.In the existing literature,the studied impulses mainly include two types:stabilized impulses and destabilized impulses.In this paper,we will study the stochastic differential systems with mixed impulses.The mixed impulses considered in this dissertation contains both stabilized and destabilized impulses.In addition,the intensity of impulses change with time.In this paper,we study the stability of a stochastic differential systems with mixed impulses by the concept of modally dependent average impulsive interval approach.By using the Lyapunov function and comparison theorem,we study the exponential stability of stochastic delay differential systems with mixed impulses.Moreover,we also consider the stability of input-to-state stability of stochastic differential systems with mixed impulses,where continuous dynamic of the impulse systems is time varying.The main contents of this dissertation are summarized as follows:The first chapter is the introduction,which contain three parts:expounding the research background and significance of the impulse stochastic differential systems;introducing the current research results at home and abroad;and finally combs the framework and content of the full text.The second chapter,when the stability of the continuous dynamic system for the impulse stochastic differential systems are determined,the exponential stability is investigated for stochastic delay differential systems with mixed impulses.The upper and lower bounds are given for the stabilized impulses and destabilized impulses,respectively.Then,the sufficient conditions of exponential stability is derived for stochastic delay differential systems with mixed impulses.In the third chapter,it has assumed that the stability of the continuous dynamic systems is time-varying.First,the input-to-state stability and the stochastic input-to-state stability of the impulse stochastic systems are considered when there are only stabilized impulses or destabilized impulses in the systems.Secondly,assuming that there are two kinds of impulses simultaneously in the systems,the input-to-state stability and the stochastic input-to-state stability of the mixed impulses stochastic differential systems are studied.Simultaneously,the upper and lower bounds of the average impulsive interval are obtained for the stabilized impulses and the destabilized impulses,respectively,and sufficient conditions for the input-to-state stability are concerned for stochastic differential systems with mixed impulses.In the fourth chapter,we have summarized the research significance and results of the full text,and also pointed out the inadequacies of this study.In addition,the future research planning and prospect are put forward.