Design of a general class of Takagi-Sugeno fuzzy control systems

The TS fuzzy controllers in this study are general: they use arbitrary continuous input fuzzy sets, any type of fuzzy logic AND, fuzzy rules with linear rule consequent and the generalized defuzzifier which contains the popular centroid defuzzifier as a special case. We prove that the general TS fuzzy controllers are nonlinear time-varying controllers with variable gains continuously changing with controllers' input variables. Using Lyapunov's linearization method, we establish a necessary and sufficient condition for analytically determining local stability of any TS fuzzy controller of the general class which controls a nonlinear plant. We utilize the stability condition to design locally stable TS fuzzy control systems.