Stability Analysis And Controller Design For T-S Fuzzy Systems

Fuzzy control theory and its application have been well developed since1985when Japanese scholar Takagi T and Sugeno M. came up with the concept of T-Sfuzzy model. Through T-S fuzzy model, a nonlinear system can be expressed as aweighted average of some linear systems, then theory of linear control system can beused in stability analysis and controller design. When there exists time delay andparameter uncertainty, system’s performance may be violated or even become unstable,in this thesis, based on Lyapunov theory and linear matrix inequality (LMI), we do aseries of further research on the stability analysis and controller design of T-S fuzzysystems.The main results of this paper are as follows:1. The state feedback controller design of T-S fuzzy system with state delay andparameter uncertainty was studied first. By using Lyapunov theory, a grouo ofsufficient conditions for the stability of the fuzzy system was given which guaranteedthe quadric performance index would not exceed some given upper bound. Based onthese results, for some commonly used membership functions (MFs), we discussedthe impact of the MFs on system’s performance, then better MFs can be selected tomake that index minimized.2. A fault tolerant H∞guaranteed cost controller was designed for T-S fuzzysystems with parameter uncertainties and state delay, when actuator fault occurred, theclosed-loop system can still be stabilized asymptotically, the H∞performance isminimized, and it guaranteed that the quadratic performance index would not exceedsome given upper bound.3. Aiming at lowering the conservativeness of traditional stability analysismethod, utilizing the knowledge that the sum of the MFs under different fuzzy rules isequal to one, some relax factor was introduced into the stability analysis of T-S fuzzysystem with parameter uncertainties. Non fragile guaranteed cost controller wasdesigned under the condition that the uncertainties of controller parameter wereadditive and multiplicative.4. By introducing the concept of staircase membership functions, the information of membership functions was taken into the stability analysis of state feedback T-S fuzzy systems with parameter uncertainties. A new group of sufficient conditions for the stability of the closed loop system was gained which are less conservative and better dynamic performance can be derived.5. The L∞output feedback control problem of T-S fuzzy model was studied, in which the controller was designed based on state observer. The L∞gain was minimized and the stability of the closed system was guaranteed. A new algorithm was given which turns the matrix inequality into LMIs and can solve the controller and the observer gain at the same time. The effectiveness of this method was proved by simulation examples.