LMI-based Stability Analysis of Discrete-time Quadratic TS Fuzzy Systems

The TS fuzzy models with polynomial rule consequents (i.e., the polynomial fuzzy models) are capable of modeling complex dynamic systems. They have attracted increasing attention in the recent years as the models of choices for the development of more advanced fuzzy controllers. In this paper, we first propose a general class of discrete-time TS fuzzy systems with quadratic rule consequents, which comprises the general TS fuzzy system as a special case. Then, by utilizing the quadratic Lyapunov function and S-procedure approach, a sufficient condition with linear matrix inequalities is established for analytically determining the local stability of the proposed system. A numerical example is given to illustrate the effectiveness and utility of our method.