The Finite-time H_∞ Control For Cascade Nonlinear Switched System

Switched systems are an important class of hybrid systems. Compared with the single system, the nature of switched systems are more rich and colorful. It plays an important role in the chemical industry, biological, traffic network and other fields. Therefore, in recent decades, more and more scholars have paid close attention to the switched system. Switched systems can be divided into linear switched systems and nonlinear switched systems. Lyapunov asymptotic stability is the basic topic in the study of switched systems. In recent years, the research on the finite-time stability of switched systems has attracted more and more attention of scholars. But among so many research results, there are few conclusions about the finite-time stability of cascaded nonlinear switched systems. This article has carried on the related research about this question. The research result is as follows:In chapter 2, the finite-time boundedness problem for a class of cascaded nonlinear switched systems is studied. By using the average dwell time method and multiple Lyapunov function method, sufficient conditions ensuring the finite-time boundedness of this systems are obtained,and a class of switching signals based on the average dwell time are designed.In chapter 3,the finite-time boundedness and finite-time stability problem for a class of discrete-time cascaded nonlinear switched systems with time-delay is discussed. Based on the average dwell time method, sufficient conditions for the finite-time stability and finite-time boundedness has been derived for these systems.In chapter 4, the finite-time H∞ control problem for a class of delayed continuous-time cascade nonlinear switched systems with disturbance is considered under asynchronous switching. Based on mode-dependent average dwell time method, the sufficient conditions for the finite-time H∞ control of these systems are achieved under asynchronous switching.