H−/L∞ fault detection observer for discrete-time Takagi-Sugeno fuzzy systems

In this paper, an H
−
/L
∞
fault detection observer is proposed for discrete-time Takagi-Sugeno (T-S) fuzzy systems. The main contribution of this paper lies as, first, the finite frequency H
−
index is used to measure the worst-case fault sensitivity. Second, unlike the common H
−
/H
∞
fault detection observer, this paper uses L
∞
norm to measure the worst effect of disturbance on residual instead of H
∞
norm. Besides, a residual evaluation is synthesized based on the Lnorm to achieve an efficient fault detection despite of the disturbance occurrence. Besides, sufficient conditions of the observer design are derived based on piecewise Lyapunov functions. The effectiveness of the proposed method is demonstrated by numerical simulations.