Generalized fuzzy Lyapunov stability analysis of discrete type II/III TSK systems

We propose a new approach for the stability analysis of discrete Sugeno types II and III fuzzy systems. The new approach uses arguments similar to those of traditional Lyapunov stability theory with positive and negative definite functions replaced by fuzzy positive definite and fuzzy negative definite functions, respectively. We introduce the concept of the equivalent fuzzy system for a cascade of two fuzzy systems. We use the cascade of a system and a fuzzy Lyapunov function candidate to derive new conditions for stability and asymptotic stability for type II and type III fuzzy systems. We apply our results to a numerical example.