Stability Analysis And Stabilization Of Nonlinear Cascaded Switched Systems

Switched systems are usually composed of several subsystems and a switching rule.The subsystem can be classified continuous time subsystems and discrete-time subsystems.The switching rules determine the switching sequence between subsystems.Switching system has important theoretical significance and wide application background,so it has been concerned by scholars for many years.Stability is the basic property of the control system,and it is the necessary premise of the system operation,Therefore,the stability of switched systems has always been a hot topic.In this paper,we study the stability of nonlinear cascade switched systems.The exponential stability and finite time stability of nonlinear cascade switched systems are studied respectively,Among them,the study of exponential stability is considered for both cases of continuous time and discrete time.The research work is summarized as follows:Firstly,the exponential stability of a class of continuous nonlinear cascade switched systems is studied.We start with a relatively simple cascade switching system,give some assumptions,and then design a state feedback controller,a conclusion that the exponential stability of the system can be given.Then the results are extended to the case where the system contains uncertainties and time-delay.By means of inequality transformation to eliminate the influence of uncertainties and time delays,we obtain a conclusion that the system is exponentially stable.The correctness of the conclusion is verified by simulation.Secondly,the exponential stability of a class of discrete nonlinear cascade switched systems is studied.Under the condition that the switching signal satisfies a certain average dwell time,the conclusion that exponential stability of discrete cascade switched systems is given.Then,the results are extended to the case where the system with time delay.The same results can be obtained for the exponential stability of the system.The correctness of the conclusion is verified by simulation.Finally,the finite time stab:ility of a class of discrete nonlinear cascade switched systems is studied.Based on the finite time stability of general linear control systems,the definition of finite time stability for switched systems is proposed.The finite time stability of a class of nonlinear cascade switched systems is studied,which considering the time delay.The correctness of the conclusion is verified by simulation.