Robust H-infinity Control Time-delay Switched Systems

Switched systems, a special and important class of hybrid systems, consist of continuous-time (discrete-time) dynamics subsystems and a set of switching rules. Switched systems show more complex dynamic characteristics with the interaction among switching, uncertainties and time delays, so a lot of issues need to be analyzed. Switched systems with uncertainties and time delays are significant both in theory and practice. In this thesis, robust stability and robust tracking control for switched systems with uncertainties and time delays are investigated. Meanwhile, average dwell-time approach and Lyapunov-Krasovskii functional method are applied. Based on existing research, some results are achieved.Firstly, robust control problem of a class of linear switched systems with constant time delays is considered. Sufficient conditions for robust control are developed by using convex combination and piecewise Lyapunov functional method. Under this condition, the closed-loop system can meet the performance with designed robust controller and switching law. The conclusion is extended to a class of linear switched systems with time-varying delays, whose derivatives are bounded.Secondly, robust stability of a class of linear switched systems with uncertainties and time-varying delays is studied. Based on existing results, average dwell-time approach and L-K functional method are utilized. Given robust stability conditions for non-switched systems, the conclusion is extended to switched systems with uncertainties and time-varying delays.Thirdly, robust tracking control of a class of linear switched systems with uncertainties and time-varying delays is investigated. An existing result is improved by using average dwell-time approach and L-K functional method. Besides, sufficient conditions for robust tracking control are emphasized, and the closed-loop system can meet the performance with designed robust tracking controller and switching law. Compared with existing results, the conditions are independent of uncertainties and easy to be verified.Forthly, robust tracking control of a class of switched fuzzy systems is developed. On the basis of average dwell-time approach and L-K functional method, the conclusion can be extended to a class of non-linear (switched fuzzy systems), and sufficient conditions for robust tracking control are proposed.Finally, the main results of this thesis are summarized, and some open problems are posed.