-/ fault detection observer design for uncertain linear systems

This paper studies fault detection problem in the finite-frequency domain for linear systems with parameter uncertainties. We design an $ H_{-}/L_{\infty } $ H−/L∞ fault detection observer to generate residual that is robust against disturbance and sensitive to a fault. In the design, we use the finite-frequency $ H_{-} $ H− performance index to measure fault sensitivity and introduce $ L_{\infty } $ L∞ performance index to measure the effect of disturbance on residual. The obtained fault detection observer exhibits a peak-to-peak disturbance attenuation performance, which provides a time-varying threshold for residual evaluation. Therefore the proposed design method integrates residual generation and threshold calculation together. To facilitate the observer design process, sufficient conditions of the proposed $ H_{-}/L_{\infty } $ H−/L∞ fault detection observer are formulated as a set of linear matrix inequalities. Numerical simulations are given to verify the effectiveness of the proposed approach.