H∞ Model Reduction for Two-Dimensional Discrete Systems in Finite Frequency Ranges

摘要

This paper examines the design problem H∞ of the reduced order model for two-dimensional (2D) discrete systems described by the Roesser model with a control input assumed to operate in a finite frequency (FF) domain. Given an asymptotically stable system; our goal is to find a stable reduced order system so that the error of the transfer functions between the original system and the reduced order is limited to a range FF. Using the well-known generalized lemma of Kalman Yakubovich Popov (gKYP) and the Finsler's lemma, sufficient conditions for the existence of the reduction of the H∞ model for different FF ranges are proposed and then unified in terms of solving a set of linear matrix inequalities (LMIs). An illustrative example is provided to show the utility and potential of the proposed results.