Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems

This paper presents a systematic procedure of fuzzy control system design t hat consists of fuzzy model construction, rule reduction, and robust compen sation for nonlinear systems. The model construction part replaces the nonl inear dynamics of a system with a generalized form of Takagi-Sugeno (T-S) f uzzy systems, which is newly developed in this paper. The generalized form has a decomposed structure for each element of Ai and Bi matrices in conseq uent parts. The key feature of this structure is that it is suitable for co nstructing IF-THEN rules and reducing the number of IF-THEN rules. The rule reduction part provides a successive procedure to reduce the number of IF- THEN rules. Furthermore, we convert the reduction error between reduced fuz zy models and a system to model uncertainties of reduced fuzzy models. The robust compensation part achieves the decay rate controller design guarante eing robust stability for the model uncertainties. Finally, two examples de monstrate the utility of the systematic procedure developed in this paper.