Zonotopic fault detection observer for discrete-time descriptor systems considering − fault sensitivity

This paper addresses a zonotopic fault detection (FD) observer for discrete-time descriptor systems subject to additive actuator faults. The considered descriptor systems are also perturbed by unknown-but-bounded uncertainties including state disturbances and measurement noise. Under a set-based framework, the effects of uncertainties and faults are separated into two state zonotopes. Based on this decomposition, the FD observer gain is designed to be robust against uncertainties and meanwhile sensitive to faults based on a $\mathcal {H}_{-} $H− index in a finite-frequency domain. Then, two linear matrix inequality (LMI) conditions are obtained to design an observer that achieves robustness and fault sensitivity at the same time. The generalised KYP lemma is applied to address the fault sensitivity condition. The optimal FD observer gain can be obtained via an offline design procedure. Finally, the proposed fault detection method is applied to a chemical mixing system and the effectiveness is shown.