Robust H;∞ filtering for 2-D FM systems: A finite frequency approach

This paper investigates the problem of robust H_∞ filtering for uncertain two-dimensional (2-D) discrete 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 finite frequency (FF) H_∞ norm of the filtering error system has a specified upper bound for all uncertainties. A generalized bounded real lemma (BRL) is first derived for FF H_∞ performance analysis of nominal 2-D FM LSS systems, and then a method, in terms of solving optimization problems with LMI constraints, is presented for robust FF H_∞ filter analysis and design. An illustrative example is given to show the improvements of the proposed filter design methods.