科研之友
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摘要
This paper deals with the problem of the optimal fault detection (FD) for linear discrete time-varying (LDTV) systems with delayed state and l(2)-norm bounded unknown input. The novelty lies in the designing of an evaluation function for the robust FD. The basic idea is to directly construct an evaluation function by using a weighted l(2)-norm of the measurement output, which achieves an optimal trade-off between the sensitivity to fault and the robustness to l(2)-norm bounded unknown input. To avoid complex computation, a feasible solution is obtained via the recursive computation by applying the orthogonal projection. It is shown that such an evaluation function provides a unified scheme for both the cases of unknown input being l(2)-norm bounded and jointly normal distribution, while a threshold may be chosen based on a priori knowledge of unknown input. A numerical example is given to demonstrate the effectiveness of the proposed method.
