Stability And H_∞Control For Switched Onlinearn Systems

Switched systems are important simplified form of hybrid systems, which havethe advantages of relatively simple structure, easy to analyze and solve practicalapplication problems. Stability is a very important property for any systems, followedby anti-disturbance capability. Many results on stability and H_∞control for switchedlinear systems have appeared and systematized. H_∞owever, there is not a fullapplication for switched nonlinear systems. Stability and H_∞control for switchednonlinear systems is studied in the paper. The main results are as follows.By using multiple storage functions method, the relation of passivity andstability are discussed for a class of switched nonlinear systems. The non-increasingcondition on the value of continuous Lyapunov-like function is relaxed. Each storagefunction is allowed to grow on the “switched on” time sequence, but the totalincrement is bounded.By using multiple storage functions method,the issue of H_∞control for a classof nonlinear systems with bounded-norm structural uncertainty and disturbance inputis studied.Each system has a storage candidate function, but the difference is whenindividual subsystem is required to satisfy robust passivity.By using CommonLyapunov function technique, single Lyapunov function technique and multipleLyapunov functions technique,the state–dependent switched laws are designed tomeet H_∞performance index.Based on hybrid feedback control theory, the problem of H_∞control for a classof cascade systems is proposed.The controller is designed via multiple Lyapunovfunction technique to stablize the systems with H_∞disturbance attenuation.Theresults show that if single controller cannot make the systems stabilizable with H_∞disturbance attenuation, the propose can be achieved via hybrid feedback. At last, the whole paper is summarized and point out the direction of futureresearch.