Control And Model Reduction For T-S Fuzzy Systems With Time Delay

Many real-world systems and processes are complicated and nonlinear, which are hard to analyze and synthesize by applying the conventional theories and approaches. Moreover, the research about the nonlinear control theory is imcomplete. Nevertheless, it has been proved that intricate nonlinear systems can be approximated to any accuracy by Takagi-Sugeno(T-S)fuzzy systems. Obviously, it's a valid method to analyze and synthesize nonlinear systems via T-S fuzzy systems. On the other hand, the time delay, which is usually deemed as one of chief sources to result in poor performance, oscillation and even instability, always emerges in a lot of engineering systems, interaction networks, financial industries and so on. Thanks to the prospective approximation ability of T-S fuzzy systems, there are more and more attractions gathered concerning fuzzy systems.The models resulted from vast physical systems and processes are complicated and high-order, which bring great difficulties to control design and stability analysis. Moreover, the results obtained are quite simple and low computational complexity concerning the control of T-S fuzzy delayed systems. Then, the conservatism is obvious in stability analysis and control design. Therefore, it prompts us to focus the problem as follows.The stability analysis of continuous-time T-S fuzzy delayed systems is investigated. By choosing appropriate Lyapunov-Krasovskii functional, combining time delay partitioning approach with the reciprocally convex technique, a new sufficient stability condition in form of linear matrix inequalities(LMIs) is developed for the delayed T-S fuzzy systems, which apparently reduces conservatism as compared with existing results.The stabilization problem of continuous-time T-S fuzzy delayed systems is considered. Based on the above less conservative stability result, the sufficient condition of fuzzy state feedback controller for T-S fuzzy delayed systems is deduced. Then, by using the parallel distributed compensation(PDC) scheme, the design of controller to make the corresponding system stable is complete.Pre-specified performance based model reduction for continuous-time T-S fuzzy delayed systems is studied. For a given stable high-order fuzzy system, by constructing suitable Lyapunov-Krasovskii functional, together with the Jensen inequality and the reciprocally convex approach, a sufficient condition of stability analysis satisfying the prescribed performance is proposed. Then, based on the projection approach, the reduced-order system is eventually obtained. The model approximation is translated into a sequential minimization problem subject to linear matrix inequality constraints by using the cone complementary algorithm.