Fault Detection Filter Design for Polytopic Uncertain Systems in Finite-Frequency Domain

This paper investigates the problem of $\mathcal{H}{\_}{-} / \mathcal{H}{\_}{\infty}$ fault detection (FD) filter design for continuous-time polytopic uncertain linear systems in the finite-frequency (FF) domain. By assuming that both disturbances and faults are restricted to FF ranges, we are interested in designing an FD filter such that the resulting filtering error system (FES) is both sensitive to faults and robust against disturbances. By using the generalized Kalman-Yakubovič-Popov (KYP) lemma, Projection lemma, and some elegant convexification procedures, sufficient conditions for synthesis of the FD filter are established by solving an optimization problem in the form of linear matrix inequalities (LMIs). Finally, simulation studies are provided to validate the effectiveness of the proposed filtering approach.