Stability analysis of discrete type-2 TSK fuzzy systems with interval uncertainty

Type-2 fuzzy systems provide good models for uncertain fuzzy systems. This paper introduces three sufficient stability conditions for Takagi-Sugeno-Kang (TSK) type-2 fuzzy systems. The main advantage of the new conditions is that they do not require the existence of a common Lyapunov function and are therefore applicable to systems with unstable consequents. Conditions are derived for stability in the sense of Lyapunov and for asymptotic stability. The use of each condition in stability testing is demonstrated using simple numerical examples where methods based on a common Lyapunov function fail.