Robust Control Design For A Class Of Switched Fuzzy Systems With Time-delay

Switched fuzzy systems refer to a class of switched systems whose subsystems are fuzzy systems. The study of switched fuzzy systems is based on switched systems theory and fuzzy systems theory, and has theoretical importance and extensive application value. In practical engineering, many factors can cause uncertainty and time-delay which may lead to instability. On the other hand, the traditional robust controllers have some certain vulnerabilities, which may also bring about the bad performance indexes, even the instability of the closed-loop system. Therefore, to study the robust stabilization problem and the non-fragile guaranteed cost problem for switched fuzzy systems with structural uncertainties and time-delay has theoretical and practical significance.In this thesis, we investigate a class of switched fuzzy systems with structural uncertainties and time-delay by employing two different methods. The main results are as follows:Firstly, the robust stabilization for a class of switched fuzzy systems with structural uncertainties and time-delay is studied. The switching law is designed via the convex combination technique, meanwhile, state feedback controllers are designed to make the switched fuzzy system asymptotically stable. Because looking for a set of feasible convex combinations is usually a NP-hard problem in the design process, we present an algorithm to find the feasible convex combinations. The effectiveness of the proposed method is demonstrated by a numerical example.Secondly, the problem of the non-fragile guaranteed cost control for a class of switched fuzzy systems with structural uncertainties and time-delay is addressed. The switching law is designed by the multiple Lyapunov functions technique, moreover, the non-fragile guaranteed cost controllers are designed not only to make the closed-loop switched fuzzy systems asymptotically stable, but also to guarantee the cost function no more than a certain upper bound. Since the different feasible solutions can result in the different cost upper bounds, we present a method to search for the optimal value of the cost function. An example is given to illustrate the effectiveness of the proposed method.Finally, the main results of the thesis are summarized. In addition, some open problems of the switched fuzzy systems and the shortcomings of the proposed methods are also discussed which deserve further study.