H-/L∞ Fault Detection Observer for Discrete-time Takagi-Sugeno Fuzzy Systems

In this paper, an H-/L-infinity 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-infinity fault detection observer, this paper uses L-infinity norm to measure the worst effect of disturbance on residual instead of H-infinity norm. Besides, a residual evaluation is synthesized based on the L-infinity norm 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.