Stability Analysis And Controller Synthesis Of Interval Type-2 T-S Fuzzy System

The stability analysis and controller design of Takagi-Sugeno(T-S) fuzzy systems have been one of the most important problems in fuzzy theory. There are many uncertainties in practice control systems, which lead to that the membership functions of T-S fuzzy system contain uncertainties. While, the type-2 fuzzy system, as an extension of the traditional fuzzy system, have great advantage in dealing with uncertainties. At present, the research on type-2 fuzzy system are mostly based on interval type-2(IT2) fuzzy set. In this paper, we study the problems of stability analysis and controller synthesis for the IT2 fuzzy system based on IT2 T-S fuzzy model approach.Firstly, based on the T-S model method, an IT2 fuzzy system is constructed. The state-feedback and output-feedback controller is designed with mismatched membership. Based on Lyapunov stability theory, the stability of closed-loop system is considered, and the existent conditions of the two kinds of controllers are obtained in terms of linear matrix inequalities(LMIs). Simulation results are provided to illustrate the effectiveness of the proposed method and the advantage on capture the uncertainties of type-2 fuzzy system. Secondly, an IT2 fuzzy controller is designed to solve the problem of actuator fault in nolinear systems. The existent conditions of fault tolerant sampling controller are obtained. The simulation results are provided to illustrate the effectiveness of the proposed method. Then, the H? output tracking control problem is considered based on IT2 fuzzy system. The existent conditions of fault tolerant sampling controller is obtained. The control procedure of continuously stirred tank reactor(CSTR) is considered and the simulation results illustrate the effectiveness of the proposed method. Finally, we summarize this paper and foresee the further research.