Robust Fault H∞H∞ Filtering Design in Finite Frequency Domain for Discrete‐Time Switched Singular Systems

The present paper focuses on the filtering problem for a class of discrete‐time switched singular (SS) systems with faults and finite frequency (FF) input signals under an arbitrary switching signal. The frequencies of the unknown input disturbance are assumed to be in a finite range. The objective is to design a linear mode‐dependent filter guaranteeing the asymptotic stability of the filtering error system with a prescribed performance bound in an FF range. Based on the generalized Kalman‐Yakubovic‐Popov lemma, multiple Lyapunov–Krasovskii functional, and some free weighting matrices are used to provide an additional degree of freedom. Efficient conditions are formulated in terms of linear matrix inequalities. The proposed method is designed in the FF domain to reduce the conservativeness generated by those designed in the entire frequency (EF) domain. Finally, numerical examples are provided to illustrate the advantages and the effectiveness of the proposed approach.