Robust Control Of Nonlinear Cascade Switched Systems With Time Delay

Nonlinear cascade switched systems are a class of important switched systems,which have widely practical application background. The interaction between discretestates and continuous states increases the difficulty in study of nonlinear switchedsystems. Nowadays, more and more scholars have pay attention to researching theproblem for an important class of nonlinear switched systems, that is, nonlinearcascade switched systems. However, the study of nonlinear cascade switched systemswith time delay is very few and the research of exponential stability for a class ofnonlinear cascade switched systems with time delay under asynchronous switching isvery limited. In this paper, by combining multiple Lyapunov function approach withaverage dwell time approach, reliable control problem and reliable H￥controlproblem for two classes of nonlinear cascade switched systems with time delay areinvestigated. The main contents are as follows:Firstly, by combing multiple Lyapunov function approach with the average dwelltime approach, the state feedback controllers are designed and the exponentialstability is obtained for the nonlinear cascade switched systems with time delay anduncertain structure in actuator faults.Secondly, the stability problem is studied for a class of nonlinear cascadeswitched systems with time delay under asynchronous switching. By using multipleLyapunov function method and average dwell time approach, the sufficient conditionswhich ensure the exponential stability under asynchronous switching for suchsystems are achieved.At last, the reliable H￥control problem for a class of nonlinear cascade switchedsystems with time-varying delay, uncertainties and disturbances is studied. By usingthe multiple Lyapunov function method, the sufficient conditions to ensure thereliable H￥control of the nonlinear cascade switched systems are obtained.