Stability Analysis and Control of Discrete Type-1 and Type-2 TSK Fuzzy Systems: Part I. Stability Analysis

This paper introduces sufficient conditions for the exponential stability of type-1 and type-2 Takagi–Sugeno–Kang (TSK) fuzzy systems. A major 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. In addition, our results include two classes of type-2 TSK systems with type-1 consequents for which no stability tests are available. The use of the conditions in stability testing is demonstrated using simple numerical examples that include cases where methods that are based on a common Lyapunov function fail. The application of the stability test to develop new controller design methodologies is presented in a separate paper (i.e., Part II).