On solutions of the matrix equations XF - AX = C and XF - A over(X, -) = C

Ai Guo Wu; Guang Ren Duan; Hai Hua Yu

doi:10.1016/j.amc.2006.06.039

On solutions of the matrix equations XF - AX = C and XF - A over(X, -) = C

Ai Guo Wu^*
, Guang Ren Duan
, Hai Hua Yu

^*Corresponding author for this work

Harbin Institute of Technology

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

50 Scopus citations

Abstract

With the help of the concept of Kronecker map, an explicit solution for the matrix equation XF - AX = C is established. This solution is neatly expressed by a symmetric operator matrix, a controllability matrix and an observability matrix. In addition, the matrix equation XF - A over(X, -) = C is also studied. An explicit solution for this equation is also proposed by means of the real representation of a complex matrix. This solution is neatly expressed by a symmetric operator matrix, two controllability matrices and two observability matrices.

Original language	English
Pages (from-to)	932-941
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	183
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2006.06.039
State	Published - 15 Dec 2006

Keywords

Controllability matrix
Kronecker map
Observability matrix
Real representation

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10.1016/j.amc.2006.06.039

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abstract = "With the help of the concept of Kronecker map, an explicit solution for the matrix equation XF - AX = C is established. This solution is neatly expressed by a symmetric operator matrix, a controllability matrix and an observability matrix. In addition, the matrix equation XF - A over(X, -) = C is also studied. An explicit solution for this equation is also proposed by means of the real representation of a complex matrix. This solution is neatly expressed by a symmetric operator matrix, two controllability matrices and two observability matrices.",

keywords = "Controllability matrix, Kronecker map, Observability matrix, Real representation",

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

year = "2006",

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day = "15",

doi = "10.1016/j.amc.2006.06.039",

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T1 - On solutions of the matrix equations XF - AX = C and XF - A over(X, -) = C

AU - Wu, Ai Guo

AU - Duan, Guang Ren

AU - Yu, Hai Hua

PY - 2006/12/15

Y1 - 2006/12/15

N2 - With the help of the concept of Kronecker map, an explicit solution for the matrix equation XF - AX = C is established. This solution is neatly expressed by a symmetric operator matrix, a controllability matrix and an observability matrix. In addition, the matrix equation XF - A over(X, -) = C is also studied. An explicit solution for this equation is also proposed by means of the real representation of a complex matrix. This solution is neatly expressed by a symmetric operator matrix, two controllability matrices and two observability matrices.

AB - With the help of the concept of Kronecker map, an explicit solution for the matrix equation XF - AX = C is established. This solution is neatly expressed by a symmetric operator matrix, a controllability matrix and an observability matrix. In addition, the matrix equation XF - A over(X, -) = C is also studied. An explicit solution for this equation is also proposed by means of the real representation of a complex matrix. This solution is neatly expressed by a symmetric operator matrix, two controllability matrices and two observability matrices.

KW - Controllability matrix

KW - Kronecker map

KW - Observability matrix

KW - Real representation

UR - https://www.scopus.com/pages/publications/33845748742

U2 - 10.1016/j.amc.2006.06.039

DO - 10.1016/j.amc.2006.06.039

M3 - 文章

AN - SCOPUS:33845748742

SN - 0096-3003

VL - 183

SP - 932

EP - 941

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

On solutions of the matrix equations XF - AX = C and XF - A over(X, -) = C

Abstract

Keywords

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