H_∞ Model Reduction of 2-D Discrete Systems

Abstract

The problem of model reduction for 2-D systems has received considerable attention due to their importance in 2-D signal and image processing applications [61][65][99][100] where it is usually desirable to represent a high-order system by a lower-order model. The essence of model reduction is to obtain a reduced order model which approximates the original system without significant error. Recently, the H _∞ model reduction method has attracted a lot of interest for 1-D systems; see [38][55][56]. The H _∞ model reduction aims to find a low-order model such that the H _∞ norm of the difference between the original model and the reduced order model is small.