This paper mainly studies the fault detection (FD) problem for linear discrete time-varying systems subject to random sensor delay. By assuming that the measurement channel is with Transmission Control Protocol (TCP), an observer-based FD filter (FDF) is provided as a residual generator via embedding the packet indicator into the filter. To construct this FDF, its design issue is formulated into two sub-problems. One is to maximize the H-/H∞ or H∞/H∞ FD performance index, which aims to enhance the ratio of fault sensitivity/disturbance attenuation. The other one is to find the filter parameter matrices such that the error between the residual and the fault is minimized in the H∞ sense. By employing stochastic analysis and introducing some adjoint operator based optimization approaches, analytical solutions to the aforementioned FDF design problem are derived via solving recursive Riccati equations. An illustrative example is given to show the effectiveness of the proposed methodologies

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Summary 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. Copyright © 2017 John Wiley & Sons, Ltd.