Stability of Takagi-Sugeno fuzzy systems

Takagi-Sugeno (T-S) fuzzy models are usually used to describe nonlinear systems by a set of IF-THEN rules that gives local linear representations of subsystems. The overall model of the system is then formed as a fuzzy blending of these subsystems. It is important to study their stability or the synthesis of stabilizing controllers. The stability of TS models has been derived by means of several methods: Lyapunov approach, switching systems theory, linear system with modeling uncertainties, etc. In this study, the uniform stability, and uniform exponential stability of a discrete time T-S model is examined. Moreover, a perturbation result and an instability condition are given. The subsystems of T-S models that is studied here are time varying and a new exponential stability theorem is given for these types of TS models by examining the existence of a common matrix sequence.