The Study On The Stability Of Impulsive Switched Systems

Switched system is an important hybrid system,which is composed of a set of continuous-time or discrete-time subsystems and a rule that orchestrates the switching among them.In practice,impulsive and time-delay phenomenon are universal,causing instability and poor performance.Because uncontrollable subsystems are unavoidable, the research of the sta-bility of switched systems with uncontrollable subsystems has important theoretical and practical value.In this paper,two problems are analyzed:Firstly, the problem of mean square exponential stability for a class of nonlinear im-pulsive stochastic switched system with mixed delays is studied.a sufficient condition for this problem is obtainded by using some integro-differential inequalities and stochastic analysis techniques.Secondly,based on the estimate on transition matrices and Gronwall inequality,we have studied the stabilization for a class of switched system with uncontrollable subsystems.