Stability Analysis Of A Class Of Nonlinear Switched Systems

Switched systems are one of the most important hybrid systems,which are composed of more than one continuous or discrete subsystems,and the corresponding switching path.The switched systems are called nonlinear switched systems,if at least one subsystem is nonlinear system.At present,there are two important methods to investigate the nonlinear switched systems,such as,Lyapunov method and average dwell time method.As for Lyapunov method,it is difficult to verify whether the switched systems have a common Lyapunov function or not,even for the linear switched system.Although the multiple Lyapunov function method is important in theory,it is difficult to be used in practice.That is to say,we need design the corresponding switching path which satisfies the conditions of the multiple Lyapunov function method in reality,it is difficult to apply to practical problem.Thus,we pay more attention to the method related to dwell time.For example,the minimum dwell time method,average dwell time method and mode-dependent average dwell time method.It should be pointed out that the dwell time methods still have some shortcomings needed to be improved.First of all,this paper improves the average dwell time method.For linear switched systems,we can strictly prove that the new method not only simplifies the conditions,but also reduces the conservative property for obtaining the lower bound of average dwell time.For nonlinear switched systems,we only prove that our method simplifies the conditions of the existing ones.Then,based on improved average dwell time method,we investigate the stability,input-to-state stability and input-to-output-state stability of the nonlinear switched systems in two cases.Compared to the existing results,this improved average method has some advantages in some cases.Finally,illustrative examples with numerical simulations are given to show the correctness and the effectiveness of our methods.