Robust $$H_{\infty }$$ H ∞ Filters for Uncertain Systems with Finite Frequency Specifications

Abstract

This paper deals with $$H_{\infty }$$ filtering problem of linear discrete-time uncertain systems with finite frequency input signals. The uncertain parameters are supposed to reside in a polytope. By applying the generalized Kalman–Yakubovich–Popov lemma, polynomially parameter-dependent Lyapunov function and some key matrices to eliminate the product terms between the filter parameters and the Lyapunov matrices, an improved condition is obtained for analyzing the $$H_{\infty }$$ performance of the filtering error system. Then sufficient condition in terms of linear matrix inequality is established for designing filters with a guaranteed $$H_{\infty }$$ filtering performance level. Finally, a numerical examples are used to demonstrate the effectiveness of the proposed method.