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

This paper is concerned with the problem of robust H_infin filtering for discrete-time switched linear systems with polytopic uncertainties in finite frequency domain. Based on generalized Kalman-Yakubovich-Popov (GKYP) lemma and switched 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_infin performance index. Compared with the existing full frequency approaches, the proposed finite frequency approach receives better results for the cases when frequency ranges of noises are known. A numerical example is given to illustrate the effectiveness of the proposed method.