chap26(英).ppt

two common positive definite matrices and to guarantee the stability of the fuzzy control system The result control law Control Rule 1: IF is about THEN Control Rule 2: IF is about THEN Total control and are the membership values of Rule 1 and Rule 2. This nonlinear control law guarantees the stability of the fuzzy control system (fuzzy model + fuzzy controller + fuzzy observer). * * 2.7.5 基于模糊状态方程模型的系统分析和设计 1、 Xiao-Jun Ma, Zeng-Qi Sun, Yan-Yan He Analysis and Design of Fuzzy Controller and Fuzzy Observer. IEEE Trans. on Fuzzy Systems. Vol.6, No.1, 1998，41-51 2、 Xiao-Jun Ma, Zeng-Qi Sun Output Tracking and Regulation of Nonlinear System Based on Takagi-Sugeno Fuzzy Model IEEE Transaction on systems,Man and Cybernetics-Part B: Cybernetics. Vol.30, No.1, 2000,77-89 3、 Xiao-Jun Ma, Zeng-Qi Sun Analysis and Design of Fuzzy Reduced –Dimensional Observer and Fuzzy Functional Observer. Fuzzy Sets and Systems 120, 2001,35-63 1. Fuzzy controller design The fuzzy state model of a plant : IF is and … and is THEN Using a standard fuzzy inference method, that is, using a singleton fuzzifier, product fuzzy inference and weighted average defuzzifier, the final state of the fuzzy system is inferred as follows: The final state of the fuzzy system can be represented as The final output of the fuzzy system is inferred as follows: For the fuzzy controller design, it is supposed that the fuzzy system is locally controllable. First, the local state feedback controllers are designed as follows. Controller Rule : IF is and … and is THEN Then the final output of the fuzzy controller is The equation for closed-loop system A sufficient condition which guarantees the stability of the fuzzy system is obtained in terms of Lyapunovs direct method. The equation above is asymptotically stable in the large if there exists a common positive defin