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Title

Generalized two-dimensional Kalman-Yakubovich-Popov lemma for discrete roesser model

Author(s)

Yang, Ran;  Xie, Lihua;  Zhang, Cishen

Abstract

Kalman-Yakubovich-Popov (KYP) lemma has played a significant role in one-dimensional systems theory. However, there has been no two-dimensional (2-D) KYP lemma in the literature, even for the infinite frequency domain. This paper develops a generalized KYP lemma for 2-D systems described by discrete Roesser model. The generalized KYP lemma relates frequency-domain properties of the 2-D system, such as positive realness and bounded realness over any given rectangular frequency domain, to a linear matrix inequality, enabling efficient computation for both the analysis and the design. As special cases of the lemma, 2-D bounded realness and positive realness are investigated. Numerical examples on the design of 2-D digital filters are given to demonstrate the relevance of the lemma.

Publication type

Journal article

Source

IEEE Transactions on Circuits and Systems I: Regular Papers, Vol. 55, no. 10 (Nov 2008), pp. 3223-3233

Publication year

2008

FOR Code(s)

0906 Electrical and Electronic Engineering

Keyword(s)

2-D systems;  Bounded and positive realness;  Digital arithmetic;  Digital filters;  Frequency domain analysis;  Kalman-Yakubovich-Popov (KYP) lemma;  Linear control systems;  Linear matrix inequalities;  Roesser model;  Turbulent flow;  Two-dimensional (2-D) digital filters;  Wave filters

Publisher

IEEE

ISSN

1057-7122

Publisher URL

http://dx.doi.org/10.1109/tcsi.2008.923284

Copyright

Copyright © 2008 IEEE. The published version of the paper is reproduced here in accordance with the copyright policy of the publisher. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.

Full text

Peer reviewed