Fault detection observer design for fuzzy systems with local nonlinear models via fuzzy Lyapunov function

Abstract

This paper concerns with the problem of designing fault detection (FD) observer for Takagi-Sugeno (T-S) fuzzy systems subject to local nonlinear models. Different from the quadratic Lyapunov function approaches, fuzzy Lyapunov function approach is applied to design the fault detection observer, and corresponding sufficient conditions are given in terms of linear matrix inequalities. In addition, combined with nonlinear local models scheme and slack variable technique, the T-S fuzzy systems have fewer fuzzy rules to reduce the computational burden. Compared with the existing results, less conservative results on existence of fuzzy fault detection observers are derived. Moreover, the designed fuzzy fault detection observer not only guarantees the residual system stability but also improves the H_ index estimation. It is noted that the H_ index is employed to measure the worst-cast fault sensitivity performance. Finally, a numerical simulation is given to illustrate the effectiveness of the designed fault detection observer.