Solution to generalized Sylvester matrix equations

Ai Guo Wu; Guang Ren Duan; Bin Zhou

doi:10.1109/TAC.2008.919562

Solution to generalized Sylvester matrix equations

Ai Guo Wu^*
, Guang Ren Duan
, Bin Zhou

^*Corresponding author for this work

Harbin Institute of Technology Shenzhen

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

56 Scopus citations

Abstract

An explicit solution to the generalized Sylvester matrix equation AX + BY = EXF is established. This solution is expressed in terms of the R-controllability matrix of (E,A,B), a generalized symmetric operator matrix and an observability matrix. Moreover, based on this solution, solutions to some other matrix equations are also derived. The results may provide great convenience for the analysis and synthesis problems related to these equations.

Original language	English
Pages (from-to)	811-815
Number of pages	5
Journal	IEEE Transactions on Automatic Control
Volume	53
Issue number	3
DOIs	https://doi.org/10.1109/TAC.2008.919562
State	Published - Apr 2008

Keywords

Explicit solutions
Generalized Sylvester equations
Parametric expressions
R-controllability matrix

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10.1109/TAC.2008.919562

Cite this

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title = "Solution to generalized Sylvester matrix equations",

abstract = "An explicit solution to the generalized Sylvester matrix equation AX + BY = EXF is established. This solution is expressed in terms of the R-controllability matrix of (E,A,B), a generalized symmetric operator matrix and an observability matrix. Moreover, based on this solution, solutions to some other matrix equations are also derived. The results may provide great convenience for the analysis and synthesis problems related to these equations.",

keywords = "Explicit solutions, Generalized Sylvester equations, Parametric expressions, R-controllability matrix",

author = "Wu, \{Ai Guo\} and Duan, \{Guang Ren\} and Bin Zhou",

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T1 - Solution to generalized Sylvester matrix equations

AU - Wu, Ai Guo

AU - Duan, Guang Ren

AU - Zhou, Bin

PY - 2008/4

Y1 - 2008/4

N2 - An explicit solution to the generalized Sylvester matrix equation AX + BY = EXF is established. This solution is expressed in terms of the R-controllability matrix of (E,A,B), a generalized symmetric operator matrix and an observability matrix. Moreover, based on this solution, solutions to some other matrix equations are also derived. The results may provide great convenience for the analysis and synthesis problems related to these equations.

AB - An explicit solution to the generalized Sylvester matrix equation AX + BY = EXF is established. This solution is expressed in terms of the R-controllability matrix of (E,A,B), a generalized symmetric operator matrix and an observability matrix. Moreover, based on this solution, solutions to some other matrix equations are also derived. The results may provide great convenience for the analysis and synthesis problems related to these equations.

KW - Explicit solutions

KW - Generalized Sylvester equations

KW - Parametric expressions

KW - R-controllability matrix

UR - https://www.scopus.com/pages/publications/42649141973

U2 - 10.1109/TAC.2008.919562

DO - 10.1109/TAC.2008.919562

M3 - 文章

AN - SCOPUS:42649141973

SN - 0018-9286

VL - 53

SP - 811

EP - 815

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 3

ER -

Solution to generalized Sylvester matrix equations

Abstract

Keywords

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