Finite-frequency memory filter design for uncertain linear discrete-time systems: A polynomially parameter-dependent approach

This paper investigates the robust filtering problem for linear uncertain systems affected by noises in restricted frequency intervals. Different from traditional filter schemes, a finite-frequency memory filter is designed to generalize conventional memoryless ones in such a way that a sequence of latest output measurements are employed for current estimation. To be specific, a memory filter is sought which ensures that for all admissible uncertainties, the filtering error system is asymptotically stable with a prescribed noise-attenuation level in the restricted frequency range. To accomplish this, the finite-frequency specification is characterized by the generalized Kalman-Yakubovich-Popov (KYP) lemma, aiming at improving the capability of noise-attenuation over the given frequency range. Moreover, the homogeneous polynomially parameter-dependent technique is adopted to facilitate filter design and reduce conservatism further. Based on the proposed scheme, we prove rigorously that additional past output measurements contribute to less conservative results. Finally, a quarter-car model with an active-suspension system is used to validate the proposed scheme.