Stability analysis for discrete fuzzy systems

Stability methods for discrete fuzzy systems based on Lyapunov stability theorem are discussed. First, we represent the fuzzy system by a Takagi-Sugeno model and we recall its stability conditions. Second, we analyze the difficulties encountered in finding a general solution for stability of such systems, and then, we study the effect of the membership functions and the dependence of the basin of attraction on the type of such functions. The methods are illustrated by examples.