Stability Analysis of Discrete TSK Type II/III Systems

We propose a new approach for the stability analysis of discrete Sugeno types II and III fuzzy systems. The approach does not require the existence of a common Lyapunov function. We introduce the concept of fuzzy positive definite and fuzzy negative definite functions. This new concept is used to replace classical positive and negative definite functions in arguments similar to those of traditional Lyapunov stability theory. We obtain the equivalent fuzzy system for a cascade of two Type II/III 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 discrete type II and type III fuzzy systems. To demonstrate the new approach, we apply it to numerical examples where no common Lyapunov function exists