DocumentCode
1125506
Title
Solution to Generalized Sylvester Matrix Equations
Author
Wu, Ai-Guo ; Duan, Guang-Ren ; Zhou, Bin
Author_Institution
Harbin Inst. of Technol., Shenzhen
Volume
53
Issue
3
fYear
2008
fDate
4/1/2008 12:00:00 AM
Firstpage
811
Lastpage
815
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
controllability; matrix algebra; set theory; controllability matrix; generalized Sylvester matrix equations; generalized symmetric operator matrix; observability matrix; Control theory; Controllability; Eigenvalues and eigenfunctions; Equations; Linear systems; Matrix decomposition; Observability; Singular value decomposition; Symmetric matrices; Explicit solutions; R-controllability matrix; generalized Sylvester equations; parametric expressions;
fLanguage
English
Journal_Title
Automatic Control, IEEE Transactions on
Publisher
ieee
ISSN
0018-9286
Type
jour
DOI
10.1109/TAC.2008.919562
Filename
4484186
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