Fault Estimation for T-S Fuzzy Systems via an L∞ Switching Observer Scheme

Ahstract- This paper addresses the fault estimation (FE) problem for T-S fuzzy systems based on the switching observer scheme. Firstly, a fuzzy FE observer with switching rules is designed, where the product of time derivative of the membership functions and Lyapunov matrix can be guaranteed to be negative definite. Furthermore, to increase the robustness of the observer against the persistence disturbance, an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{\infty}$</tex> performance index is considered for synthesizing the FE observer. Then, based on the Lyapunov stability analysis method and the average dwell-time technique, the synthesis conditions of the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{\infty}$</tex> FE switching observer are given in terms of linear matrix inequalities (LMIs). The merit of the proposed method is that by using the switching rules, the constraint in the conventional methods, where the state should be limited into a local area, can be removed. Finally, an example is given to show the efficacy of the presented FE scheme.