New Approach to H∞ Filtering for Uncertain Discrete-Time Linear Systems in Finite Frequency Domain

The problem of finite frequency (FF) H-infinity full-order filtering design for discrete-time linear systems, with polytopic uncertainties, is investigated in this paper. Based on the generalized Kalman-Yakubovich-Popov (GKYP) lemma and a parameter dependent Lyapunov function, a set of sufficient conditions for the existence of the H-infinity filter are established in terms of matrix inequalities, ensuring that the filtering error system is stable and the H-infinity attenuation level from disturbance to the estimation error is minimized in the FF domain of the external disturbances. Then, in order to linearize and relax the obtained matrix inequalities, we apply Finsler's lemma twice, which provides extra degrees of freedom in optimizing the guaranteed H-infinity performance, and we show how we can calculate the filter gain matrices by using these conditions. Numerical example is given to illustrate the effectiveness and the less conservatism of the proposed approach in comparison with the existing methods.