An Approach for Stability Analysis of T-s Fuzzy Systems via Piecewise Quadratic Stability

This paper presents a new approach for the stability analysis of TakagiSugeno (T-S) fuzzy systems. An idea is investigated to use piecewise quadratic Lyapunov function with low amount of computations. This class of Lyapunov function candidates is much richer than the common quadratic Lyapunov function. By exploiting the piecewise continuous Lyapunov function, we derive stability conditions that can be verified via convex optimization over linear matrix inequalities (LMIs) or bilinear matrix inequalities (BMIs). This idea will be used to derive some sufficient stability conditions for output feedback controller, parallel distributed compensation (PDC) and dynamic parallel distributed compensation (DPDC). Independence of this method of finding only one positive definite matrix that makes this method highly applicable, has less computation. Also, independence of these fuzzy sets to be normalized and their shapes make this method more useful. A numerical example which is given illustrates the effectiveness of the proposed method.