Robust finite frequency filtering for uncertain 2-D systems: The FM model case

This paper is concerned with the problem of robust finite frequency (FF) H ∞ filtering for uncertain two-dimensional (2-D) discrete-time systems in the Fornasini–Marchesini local state-space (FM LSS) model with polytopic uncertain parameters. The goal of the paper is to design filters such that the FF H ∞ norm of the filtering error system has a specified upper bound for all uncertainties. In light of a recently developed generalized bounded real lemma, a linear matrix inequality-based approach is proposed for robust FF H ∞ filter analysis and design. It is demonstrated that the presented approach to robust FF H ∞ filter design covers the latest standard H ∞ filtering result. Moreover, it is shown that the existing results specialized for the Roesser model, when applied to the FM LSS model through a model transformation, are much more restrictive than the proposed results in the paper, further justifying this work.