Fault detection for singular multiple time-delay systems with application to electrical circuit

In this paper, an H−/H∞ fault detection (FD) filter is designed for linear singular systems with multiple state delays. System faults and unknown disturbances are assumed to reside in finite frequency ranges. By combining the Parseval theorem and the strict S-procedure, both time domain and frequency domain approaches are used to formulate a new delay-dependent finite frequency bounded real lemma (BRL), which includes some existing results as special cases. Based on the obtained BRL, convex FD filter design conditions are derived in terms of solving a set of linear matrix inequalities (LMIs). The effectiveness of the proposed finite frequency FD method is illustrated through a simulation example on the electrical circuit.