Unified parametrization for the solutions to the polynomial diophantine matrix equation and the generalized sylvester matrix equation

Bin Zhou; Guang Ren Duan; Zhi Bin Yan

doi:10.1109/CCDC.2008.4598097

Unified parametrization for the solutions to the polynomial diophantine matrix equation and the generalized sylvester matrix equation

Bin Zhou^*
, Guang Ren Duan
, Zhi Bin Yan

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

The polynomial Diophantine matrix equation and the generalized Sylvester matrix equation are important for controller design in frequency domain linear system theory and time domain linear system theory, respectively. By using the so-called generalized Sylvester mapping, right coprime factorization and Bezout identity associated with certain polynomial matrices, we present in this note a unified parametrization for the solutions to both of these two classes of matrix equations. Moreover, it is shown that solutions to the generalized Sylvester matrix equation can be obtained if solutions to the Diophantine matrix equation are available. The results disclose a relationship between the polynomial Diophantine matrix equation and generalized Sylvester matrix equation that are respectively studied and used in frequency domain linear system theory and time domain linear system theory.

Original language	English
Title of host publication	Chinese Control and Decision Conference, 2008, CCDC 2008
Pages	4075-4080
Number of pages	6
DOIs	https://doi.org/10.1109/CCDC.2008.4598097
State	Published - 2008
Event	Chinese Control and Decision Conference 2008, CCDC 2008 - Yantai, Shandong, China Duration: 2 Jul 2008 → 4 Jul 2008

Publication series

Name	Chinese Control and Decision Conference, 2008, CCDC 2008

Conference

Conference	Chinese Control and Decision Conference 2008, CCDC 2008
Country/Territory	China
City	Yantai, Shandong
Period	2/07/08 → 4/07/08

Keywords

Coprime factorization and bezout identity
Diophantine matrix equation
Generalized sylvester mapping
Generalized sylvester matrix equation
Linear system theory
Parametrization

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10.1109/CCDC.2008.4598097

Cite this

Zhou, B., Duan, G. R., & Yan, Z. B. (2008). Unified parametrization for the solutions to the polynomial diophantine matrix equation and the generalized sylvester matrix equation. In Chinese Control and Decision Conference, 2008, CCDC 2008 (pp. 4075-4080). Article 4598097 (Chinese Control and Decision Conference, 2008, CCDC 2008). https://doi.org/10.1109/CCDC.2008.4598097

@inproceedings{b06a3276d43d40c68462cf787f95bbb8,

title = "Unified parametrization for the solutions to the polynomial diophantine matrix equation and the generalized sylvester matrix equation",

abstract = "The polynomial Diophantine matrix equation and the generalized Sylvester matrix equation are important for controller design in frequency domain linear system theory and time domain linear system theory, respectively. By using the so-called generalized Sylvester mapping, right coprime factorization and Bezout identity associated with certain polynomial matrices, we present in this note a unified parametrization for the solutions to both of these two classes of matrix equations. Moreover, it is shown that solutions to the generalized Sylvester matrix equation can be obtained if solutions to the Diophantine matrix equation are available. The results disclose a relationship between the polynomial Diophantine matrix equation and generalized Sylvester matrix equation that are respectively studied and used in frequency domain linear system theory and time domain linear system theory.",

keywords = "Coprime factorization and bezout identity, Diophantine matrix equation, Generalized sylvester mapping, Generalized sylvester matrix equation, Linear system theory, Parametrization",

author = "Bin Zhou and Duan, \{Guang Ren\} and Yan, \{Zhi Bin\}",

year = "2008",

doi = "10.1109/CCDC.2008.4598097",

language = "英语",

isbn = "9781424417346",

series = "Chinese Control and Decision Conference, 2008, CCDC 2008",

pages = "4075--4080",

booktitle = "Chinese Control and Decision Conference, 2008, CCDC 2008",

note = "Chinese Control and Decision Conference 2008, CCDC 2008 ; Conference date: 02-07-2008 Through 04-07-2008",

}

Zhou, B , Duan, GR & Yan, ZB 2008, Unified parametrization for the solutions to the polynomial diophantine matrix equation and the generalized sylvester matrix equation. in Chinese Control and Decision Conference, 2008, CCDC 2008., 4598097, Chinese Control and Decision Conference, 2008, CCDC 2008, pp. 4075-4080, Chinese Control and Decision Conference 2008, CCDC 2008, Yantai, Shandong, China, 2/07/08. https://doi.org/10.1109/CCDC.2008.4598097

Unified parametrization for the solutions to the polynomial diophantine matrix equation and the generalized sylvester matrix equation. / Zhou, Bin ; Duan, Guang Ren ; Yan, Zhi Bin.
Chinese Control and Decision Conference, 2008, CCDC 2008. 2008. p. 4075-4080 4598097 (Chinese Control and Decision Conference, 2008, CCDC 2008).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Unified parametrization for the solutions to the polynomial diophantine matrix equation and the generalized sylvester matrix equation

AU - Zhou, Bin

AU - Duan, Guang Ren

AU - Yan, Zhi Bin

PY - 2008

Y1 - 2008

N2 - The polynomial Diophantine matrix equation and the generalized Sylvester matrix equation are important for controller design in frequency domain linear system theory and time domain linear system theory, respectively. By using the so-called generalized Sylvester mapping, right coprime factorization and Bezout identity associated with certain polynomial matrices, we present in this note a unified parametrization for the solutions to both of these two classes of matrix equations. Moreover, it is shown that solutions to the generalized Sylvester matrix equation can be obtained if solutions to the Diophantine matrix equation are available. The results disclose a relationship between the polynomial Diophantine matrix equation and generalized Sylvester matrix equation that are respectively studied and used in frequency domain linear system theory and time domain linear system theory.

AB - The polynomial Diophantine matrix equation and the generalized Sylvester matrix equation are important for controller design in frequency domain linear system theory and time domain linear system theory, respectively. By using the so-called generalized Sylvester mapping, right coprime factorization and Bezout identity associated with certain polynomial matrices, we present in this note a unified parametrization for the solutions to both of these two classes of matrix equations. Moreover, it is shown that solutions to the generalized Sylvester matrix equation can be obtained if solutions to the Diophantine matrix equation are available. The results disclose a relationship between the polynomial Diophantine matrix equation and generalized Sylvester matrix equation that are respectively studied and used in frequency domain linear system theory and time domain linear system theory.

KW - Coprime factorization and bezout identity

KW - Diophantine matrix equation

KW - Generalized sylvester mapping

KW - Generalized sylvester matrix equation

KW - Linear system theory

KW - Parametrization

UR - https://www.scopus.com/pages/publications/52349117584

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DO - 10.1109/CCDC.2008.4598097

M3 - 会议稿件

AN - SCOPUS:52349117584

SN - 9781424417346

T3 - Chinese Control and Decision Conference, 2008, CCDC 2008

SP - 4075

EP - 4080

BT - Chinese Control and Decision Conference, 2008, CCDC 2008

T2 - Chinese Control and Decision Conference 2008, CCDC 2008

Y2 - 2 July 2008 through 4 July 2008

ER -

Unified parametrization for the solutions to the polynomial diophantine matrix equation and the generalized sylvester matrix equation

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