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 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.

中文翻译：

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考虑到故障敏感性的离散时间描述符系统的带状故障检测观测器

本文讨论了受加性执行器故障影响的离散时间描述符系统的区域故障检测 (FD) 观测器。所考虑的描述符系统也受到未知但有界不确定性的干扰，包括状态干扰和测量噪声。在基于集合的框架下，不确定性和断层的影响被分为两种状态带位。基于这种分解，FD 观测器增益被设计为对不确定性具有鲁棒性，同时基于有限频域中的指标对故障敏感。然后，获得两个线性矩阵不等式 (LMI) 条件来设计同时实现鲁棒性和故障灵敏度的观测器。应用广义 KYP 引理来解决故障敏感性条件。最佳 FD 观测器增益可以通过离线设计程序获得。最后，将所提出的故障检测方法应用于化学混合系统，并显示了有效性。