New Discrete Tanaka Sugeno Kang Fuzzy Systems Characterization and Stability Domain

Abstract

In this paper, an analytical approach to characterize discrete Tanaka Sugeno Kang (TSK) fuzzy systems is presented. This characterization concerns the choice of the adequate conjunctive operator between input variables of discrete TSK fuzzy models, t-norm, and its impact on stability domain estimation. This new approach is based on stability conditions issued from vector norms corresponding to a vector-Lyapunov function. In particular, second order discrete TSK models are considered and this work concludes that Zadeh’s t-norm, logic product min, gives the largest estimation of stability domain.