The analytical general solutions to the higher-order Sylvester matrices equation

Hai Hua Yu; Guang Ren Duan

The analytical general solutions to the higher-order Sylvester matrices equation

Hai Hua Yu^*
, Guang Ren Duan

^*Corresponding author for this work

School of Astronautics

Heilongjiang University
Harbin Institute of Technology

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

11 Scopus citations

Abstract

Three completely analytical parametric solutions to the matrices equation A_m1VJ^m1 + ⋯ + A₁VJ+A₀V = B_m2WJ^m2 + ⋯ + B₁WJ+B₀W are presented. These solutions are expressed in terms of parameter vectors, which provide the design degrees of freedom. These approaches do not require the eigenvalues of J to be distinct or to be different from the roots of A(s). Moreover, the obtained solutions contain only numerical matrix calculations, which provide convenience for the computation of these solutions in applications. A numerical example validates the proposed approaches.

Original language	English
Pages (from-to)	698-702
Number of pages	5
Journal	Kongzhi Lilun Yu Yingyong/Control Theory and Applications
Volume	28
Issue number	5
State	Published - May 2011

Keywords

Analytical general solution
Eigenvalue
Jordan canonical form
Matrix equation

Cite this

@article{f0cef263dd58440fb0fcbfd34a5b21ff,

title = "The analytical general solutions to the higher-order Sylvester matrices equation",

abstract = "Three completely analytical parametric solutions to the matrices equation Am1VJm1 + ⋯ + A1VJ+A0V = Bm2WJm2 + ⋯ + B1WJ+B0W are presented. These solutions are expressed in terms of parameter vectors, which provide the design degrees of freedom. These approaches do not require the eigenvalues of J to be distinct or to be different from the roots of A(s). Moreover, the obtained solutions contain only numerical matrix calculations, which provide convenience for the computation of these solutions in applications. A numerical example validates the proposed approaches.",

keywords = "Analytical general solution, Eigenvalue, Jordan canonical form, Matrix equation",

author = "Yu, \{Hai Hua\} and Duan, \{Guang Ren\}",

year = "2011",

month = may,

language = "英语",

volume = "28",

pages = "698--702",

journal = "Kongzhi Lilun Yu Yingyong/Control Theory and Applications",

issn = "1000-8152",

publisher = "South China University of Technology",

number = "5",

}

TY - JOUR

T1 - The analytical general solutions to the higher-order Sylvester matrices equation

AU - Yu, Hai Hua

AU - Duan, Guang Ren

PY - 2011/5

Y1 - 2011/5

N2 - Three completely analytical parametric solutions to the matrices equation Am1VJm1 + ⋯ + A1VJ+A0V = Bm2WJm2 + ⋯ + B1WJ+B0W are presented. These solutions are expressed in terms of parameter vectors, which provide the design degrees of freedom. These approaches do not require the eigenvalues of J to be distinct or to be different from the roots of A(s). Moreover, the obtained solutions contain only numerical matrix calculations, which provide convenience for the computation of these solutions in applications. A numerical example validates the proposed approaches.

AB - Three completely analytical parametric solutions to the matrices equation Am1VJm1 + ⋯ + A1VJ+A0V = Bm2WJm2 + ⋯ + B1WJ+B0W are presented. These solutions are expressed in terms of parameter vectors, which provide the design degrees of freedom. These approaches do not require the eigenvalues of J to be distinct or to be different from the roots of A(s). Moreover, the obtained solutions contain only numerical matrix calculations, which provide convenience for the computation of these solutions in applications. A numerical example validates the proposed approaches.

KW - Analytical general solution

KW - Eigenvalue

KW - Jordan canonical form

KW - Matrix equation

UR - https://www.scopus.com/pages/publications/79960065770

M3 - 文章

AN - SCOPUS:79960065770

SN - 1000-8152

VL - 28

SP - 698

EP - 702

JO - Kongzhi Lilun Yu Yingyong/Control Theory and Applications

JF - Kongzhi Lilun Yu Yingyong/Control Theory and Applications

IS - 5

ER -

The analytical general solutions to the higher-order Sylvester matrices equation

Abstract

Keywords

Other files and links

Fingerprint

Cite this