Stability of slowly varying Takagi-Sugeno fuzzy systems using zero exclusion theorem

Abstract

A method for stability analysis of Takagi-Sugeno fuzzy systems with linear transfer submodels in the consequents of rules is presented. The Takagi-Sugeno fuzzy model of a plant is supposed where the consequents of rules are linear input-output subsystems. A PDC controller with dynamic output feedback is used. The method can be applied if the parameters of the model do not vary too rapidly. The analysis is based on a stability test of corresponding frozen-time systems using the fact that those systems are linear. Stability analysis of such uncertain linear systems is performed testing the corresponding value sets using the zero exclusion theorem. Overbounding the value set by a convex polygon a sufficient condition of stability is obtained. The method can be also used for stability analysis of an uncontrolled Takagi-Sugeno fuzzy model of a plant. As an arbitrary stability region can be chosen the procedure can be used for both continuous-time and discrete-time systems.