Control And Stability Analysis Of Fuzzy Systems Based On T-S Model

Fuzzy control is an important approach in intelligent control. The research of fuzzy control theory includes a series of main problems, such as the stability and robustness analysis, the system design approach and the improvement of the system performance etc. Although many academic achievements based on T-S fuzzy model have been achieved, there are still some questions waiting to make further research such as guaranteed cost control, controller design when the states are not available and static output feedback control. The main contribution in this paper is to solve the above problems partially by using matrix inequality theory and linear matrix inequality (LMI) approach. The main works of this dissertation are following.The guaranteed cost control via memoryless feedback controllers is studied for fuzzy systems including guaranteed cost control of uncertain fuzzy systems with time-delay, uncertaint discrete fuzzy systems and uncertain discrete fuzzy systems with time-delay. The feedback control laws are obtained through solving LMIs. This method not only guarantees stability, but also minimizes an upper bound.The robust fuzzy control for nonlinear uncertain systems with time-delay and nonlinear uncertain discrete systems in the presence of parametric uncertainties and the state variables unavailable for measurement is addressed. The Tagaki-Sugeno (T-S) discrete fuzzy model system with parametric uncertainties is adopted for modeling the nonlinear systems and establishing fuzzy observer. Sufficient conditions are derived for robust stabilization in the sense of Lyapunov asymptotic stability and are formulated in the format of LMIs. The effectiveness of the proposed fuzzy controller and fuzzy observer is finally demonstrated through numerical simulations on an inverted pendulum system.The output feedback stabilization is addressed for a class of uncertain fuzzy dynamic systems with time-delay. The T-S fuzzy model is used to represent an uncertain nonlinear system with time-delay. Sufficient conditions for output feedback stabilizability are established in the form of matrix inequality. An iterative linear matrix inequality (ILMI) algorithm is also given.