The Exponential Stability Of The Linear Time-varying Switched Systems

The hybrid system is a class of a complex systems,it is composed by continuous dynamic and discrete dynamic which effect each other.Recently,it becomes the one hotspot issues of control field.As an important and familiar hybrid system,the switched systems gain the more extentive application with the rapid development of the computer technique.In this paper,the exponential stability of linear time-varying switched systems under certain assumptions is studied mainly.It gives a sufficient condition of the exponential stability for the continuous-time linear slow-varying switched systems under arbitrary switching laws by searching for the common Lyapunov function,and it discusses the exponential stability for the continuous-time linear switched systems with nonlinear perturbed terms.Then it extends the foregoing results to the discrete switched systems accordingly.