Research On Stability And H_? Control Problem For A Class Of Discrete Nonlinear Switched Systems

The stability is the primary condition of its normal operation for any system,and the second is the anti-interference ability.Research on the stability and H_? control problem of linear switched systems and nonlinear continuous switched systems has a lot of achievements,but research on stability and H_? control problem of switched nonlinear systems is less.In this paper,the stability and H_? control problem of a class of discrete-time switched nonlinear systems are studied.The main contents of this paper are as follows:1.The problems of stability and stabilization for a class of discrete-time switched nonlinear systems are studied.Three parts are included here.The first part focuses on the cases that all the subsystems are stable and partial systems are stable,by using multiple Lyapunov functions and average dwell time technique,sufficient conditions of exponential stability are obtained,respectively.When none of the subsystems is stable,using the proposed new single Lyapunov method and the multiple Lyapunov method,respectively,we present sufficient conditions which guarantee the asymptotically stability of the switched systems by designing the state-dependent switching laws in the second part.In addition,unlike the conventional single Lyapunov function method,the new single Lyapunov function method relaxes the requirement for the system matrix to meet the convex combination conditions.The problem of controller design for the asymptotically stability of the switched systems under arbitrary switching is studied in the third part.Two kinds of state feedback controllers that one is linear and the other is nonlinear are designed,and the effectiveness of the controllers is verified by using the switched Lyapunov function method.2.For the asynchronous switching circumstance induced by the lag of switching signals of the controllers,the stabilization conditions for the system and the designing method of state feedback controllers are given via the average dwell time approach.3.Firstly,the l₂ gain problem of the discrete nonlinear switched ?-systems is studied here.For the given performance index,we design the linear state feedback controllers and find the conditions of l₂ gain for the switching system under arbitrary switching.Secondly,the H_? state tracking control problem for discrete nonlinear switching ?-systems is considered using switched Lyapunov method.State feedback controllers are designed and sufficient conditions are given such that the H_? moded reference tracking performance is guaranteed under arbitrary switching.