Robust fault detection for uncertain discrete-time systems subject to signal-to-noise ratio constrained channels

In this paper, the robust fault detection problem for uncertain discrete-time systems subject to signal-to-noise ratio (SNR) constrained communication channels is investigated. An optimal residual generation with no modeling errors is used as the reference residual model of robust fault detection filter design for the uncertain discrete-time systems with both modeling errors and SNR constraints; then, the robust fault detection filter design is formulated as an optimal H∞ filtering problem. In order to detect faults, a norm-based residual evaluation function is proposed, and an on-line dynamic threshold and its computing method are also given. Based on the notable Chebyshev׳s inequality, the false alarm rate is used to evaluate the performance of the designed threshold. The validity of the proposed method is illustrated by a numerical example.