The 2-D σ-reciprocal system for model reduction

Author

Xie, Baohui ; Syrmos, Vassilis L.

Author_Institution

Dept. of Electr. Eng., Hawaii Univ., Honolulu, HI, USA

Volume

44

Issue

11

fYear

1997

fDate

11/1/1997 12:00:00 AM

Firstpage

1056

Lastpage

1064

Abstract

In this paper we define the σ-reciprocal system of a two-dimensional (2-D) linear time-invariant system represented by the Roesser model. We introduce the 2-D σ-reciprocal system and show that the 2-D generalized singular perturbational approximation (2-D GSPA) is related to direct truncation of its σ-reciprocal system. The stability analysis and the H_∞-norm of the error for the GSPA reduction of 2-D denominator separable systems are presented. A model reduction algorithm based on the analysis of the σ-reciprocal system is given for 2-D systems. Simulation results show that the H_∞-norm of the error of the 2-D GSPA reduction is less or equal to the H_∞-norm of the error if the 2-D singular perturbational approximation (2-D SPA) or the direct truncation method are used

Keywords

linear systems; multidimensional systems; reduced order systems; singularly perturbed systems; stability; 2D σ-reciprocal system; 2D denominator separable systems; GSPA reduction; H_∞-norm; Roesser model; direct truncation; generalized singular perturbational approximation; linear time-invariant system; model reduction algorithm; stability analysis; Algorithm design and analysis; Approximation error; Digital images; Filters; Frequency domain analysis; Magnetic separation; Reduced order systems; Stability; State-space methods; Two dimensional displays;

fLanguage

English

Journal_Title

Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on

Publisher

ieee

ISSN

1057-7122

Type

jour

DOI

10.1109/81.641768

Filename

641768