H∞ Fault Detection Filter Design for Linear Continuous-Time Delay Systems in the Finite-Frequency Domain

For linear continuous-time systems subject to delays, this work constructs an H∞-based fault detection filter operating over a prescribed frequency range. By employing finite-frequency techniques, the design problem of the filter is recast as a delay-dependent H∞ filter design issue. The delay-dependent fault detection filter designed by this method satisfies the prescribed performance index H∞ over the specified frequency range. To characterize the finite-frequency features of faults and disturbances, the generalized KYP lemma is employed to establish a set of LMI-based sufficient conditions for filter existence. This avoids the complexity and potential inaccuracy introduced by weighting functions in existing approaches. Simulation results demonstrate that, under identical fault conditions, the proposed delay-dependent approach achieves better detection capability than the delay-independent approach.