Finite frequency H∞H∞ filtering for uncertain discrete-time switched linear systems

This paper is concerned with the problem of robust H∞H∞ filtering for discrete-time switched linear systems with polytopic uncertainties in the finite frequency domain. Based on the generalized Kalman–Yakubovich–Popov (GKYP) lemma and switched parameter-dependent Lyapunov functions, a switched full-order filter is designed such that the corresponding filtering error system is asymptotically stable and satisfies a prescribed finite frequency H∞H∞ performance index. Compared with the existing full frequency approaches, the proposed finite frequency one receives better results for the cases in which the frequency ranges of noises are known. A numerical example is given to illustrate the effectiveness of the proposed method.