Research On The ISS Stability Of A Class Of Continuous/discrete Pulse Switching Systems

Hybrid system is a very complex system,which mainly includes two parts:continuous subsystems and discrete subsystems.Impulsive system is an important part in researching hy-brid systems.Impulsive systems attracted considerable attention of researchers based on the characteristics of instantaneous state jump.Switched system,which via some subsystems and some switching rules to interact and coordinate,is another important part in researching hy-brid systems.Because impulsive phenomena often occurs in the modeling of dynamic switched systems,we combine them to discuss jointly,i.e.impulsive switched systems.The concept of input-to-state stability(ISS)was first introduced by Sontag.It has been proved that the input-to-state stability(ISS)is the effective tool for describing external input effects in the past decades.This paper investigates the input-to-state stability of impulsive switched systems by employing the method of multiple Lyapunov methods.The main results of this paper can be summarized as follows:1)Input-to-state stability of continuous impulsive switched systemsThis paper investigates the pth moment input-to-state stability(ISS)of continuous impul-sive switched systems with delayed impulses.By employing the method of multiple Lyapunov-Krasovskii functions and the uniformly exponentially stable function,some sufficient condition-s were presented to ensure the p-ISS of the systems.In other words,the relationship between impulsive frequency,delayed impulsive and the upper bound of derivatives of Lyapunov func-tions are established.If the continuous stochastic synamics are stable,and the impulses destroy the stability,the system can still be stable under the certain conditions.In this chapter,we extend the derivative of Lyapunov functions to sign-changing time-varying function,all subsys-tems can be unstable and we take the effect of the delayed impulses into account.Finally,an example is provided to illustrate the effectiveness of the results.2)Input-to-state stability of discrete impulsive switched systemsThis chapter investigates the input-to-state stability(ISS)of discrete impulsive switched systems.By employing the method of Lyapunov functions and the admissible edge-dependent average dwell time(AED-ADT).The upper bound of admissible edge-dependent average d-well time(AED-ADT)?_j~a,_iis constructed by the estimation coefficient of the derivative of the Lyapunov functions and Lyapunov functions at impulsive time.Input-to-state stability of the systems were derived at the condition that the stable subsystems coexist with the unstable sub-systems.Finally,an example is provided to illustrate the effectiveness of the results.