Parametric solutions to Sylvester-conjugate matrix equations

Ai Guo Wu; Lingling Lv; Guang Ren Duan; Wanquan Liu

doi:10.1016/j.camwa.2011.08.034

Parametric solutions to Sylvester-conjugate matrix equations

Ai Guo Wu^*
, Lingling Lv
, Guang Ren Duan
, Wanquan Liu

^*Corresponding author for this work

School of Astronautics

Harbin Institute of Technology Shenzhen
North China Institute of Water Conservancy and Hydroelectric Power
Curtin University

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

By two recently proposed operations with respect to complex matrices, a simple explicit solution to the Sylvester-conjugate matrix equation is given in a finite series form. The obtained solution can also be equivalently expressed in terms of the so-called controllability-like matrix and observability-like matrix. The proposed solution can provide all the degrees of freedom which is represented by a free parameter matrix. An illustrative example is employed to show the effectiveness of the proposed method.

Original language	English
Pages (from-to)	3317-3325
Number of pages	9
Journal	Computers and Mathematics with Applications
Volume	62
Issue number	9
DOIs	https://doi.org/10.1016/j.camwa.2011.08.034
State	Published - Nov 2011

Keywords

Controllability-like matrix
Explicit solution
Observability-like matrix
Sylvester-conjugate matrix equation

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10.1016/j.camwa.2011.08.034

Cite this

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title = "Parametric solutions to Sylvester-conjugate matrix equations",

abstract = "By two recently proposed operations with respect to complex matrices, a simple explicit solution to the Sylvester-conjugate matrix equation is given in a finite series form. The obtained solution can also be equivalently expressed in terms of the so-called controllability-like matrix and observability-like matrix. The proposed solution can provide all the degrees of freedom which is represented by a free parameter matrix. An illustrative example is employed to show the effectiveness of the proposed method.",

keywords = "Controllability-like matrix, Explicit solution, Observability-like matrix, Sylvester-conjugate matrix equation",

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AU - Lv, Lingling

AU - Duan, Guang Ren

AU - Liu, Wanquan

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Y1 - 2011/11

N2 - By two recently proposed operations with respect to complex matrices, a simple explicit solution to the Sylvester-conjugate matrix equation is given in a finite series form. The obtained solution can also be equivalently expressed in terms of the so-called controllability-like matrix and observability-like matrix. The proposed solution can provide all the degrees of freedom which is represented by a free parameter matrix. An illustrative example is employed to show the effectiveness of the proposed method.

AB - By two recently proposed operations with respect to complex matrices, a simple explicit solution to the Sylvester-conjugate matrix equation is given in a finite series form. The obtained solution can also be equivalently expressed in terms of the so-called controllability-like matrix and observability-like matrix. The proposed solution can provide all the degrees of freedom which is represented by a free parameter matrix. An illustrative example is employed to show the effectiveness of the proposed method.

KW - Controllability-like matrix

KW - Explicit solution

KW - Observability-like matrix

KW - Sylvester-conjugate matrix equation

UR - https://www.scopus.com/pages/publications/80054694298

U2 - 10.1016/j.camwa.2011.08.034

DO - 10.1016/j.camwa.2011.08.034

M3 - 文章

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VL - 62

SP - 3317

EP - 3325

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

IS - 9

ER -

Parametric solutions to Sylvester-conjugate matrix equations

Abstract

Keywords

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