Fault diagnosis and compensation for two-dimensional discrete time systems with sensor faults and time-varying delays

A fault diagnosis and compensation problem for two-dimensional discrete time systems with time-varying state delays is studied in this paper. The concerned two-dimensional systems are described by the Fornasisi–Marchesini second model and are subject to unknown disturbances. First, a fault detection and diagnosis module is designed to obtain the information on sensor faults; a new fault detection and diagnosis integrated design, using the observer based on descriptor system approach, is proposed to detect and estimate the sensor faults. The integrated design can maximize the fault detection rate for a given false alarm rate. Sufficient conditions for the existence of the integrated fault detection and diagnosis design are derived in the context of norm evaluation and provided in terms of matrix inequalities. Second, a fault-tolerant control module is proposed upon an existing output feedback controller. When the sensor fault occurs, the faulty measurement can be identified and corrected by the proposed fault detection and diagnosis module. In this case, the feedback controller can guarantee the performance of the closed-loop system even when encountering sensor faults. Finally, the proposed method is applied to a thermal process to illustrate its effectiveness.