Delay-Dependent Analysis And Synthesis For T-S Fuzzy Systems

In this paper, the delay-dependent stability analysis and synthesis of the uncertain T-S fuzzy model are concerned. Both relaxation matrix method and interval time-varying delay method are used in the full paper to get a less conservative result.In the first chapter, fuzzy logic control, Takagi-Sugeno fuzzy model and the procedures of T-S fuzzy method are introduced. From the procedures, the advantages of this method can be seen, that is, the well-established linear system theory can be applied for the fuzzy systems.In the second chapter, delay-dependent stability analysis, H_∞ performance control and the guaranteed cost control for the uncertain T-S fuzzy model are investigated. Based on a Lyapunov-Krassovskii approach, sufficient stability conditions are proposed, and then fuzzy controller is designed via so-called parallel distribute compensation(PDC) technique to stabilize the plant. In this chapter, the sufficient conditions for the exponential stability can also been obtained under an H_∞ performance or with the guaranteed cost performance.In the third chapter of this paper, delay-dependent stability analysis via observer-based control and dynamic output feedback control are studied. It should be pointed out that in all the past literatures, if the Lyapunov-Krasovskii approach was used, they all had the assumption that the derivation of the time-varying delay must be less than one. But in this paper, this assumption is no longer a necessary condition, that is, we can control the T-S fuzzy systems with fast time-varying delays. By using the LMI toolbox, the maximum allowable delay bound of the time delay can be easily obtained. At the end of every section, numerical examples are given to illustrate the more effectiveness and less conservativeness of the proposed method.