Solvability conditions and general solution for mixed Sylvester equations

In this paper, we give some necessary and sufficient solvability conditions for the mixed Sylvester matrix equations, and parameterize general solution when it is solvable. Moreover, we investigate the maximal and minimal ranks of the general solution, and maximal and minimal ranks and inertias of H...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 49; no. 9; pp. 2713 - 2719
Main Authors Wang, Qing-Wen, He, Zhuo-Heng
Format Journal Article
LanguageEnglish
Published Kidlington Elsevier Ltd 01.09.2013
Elsevier
Subjects
Algebra
Applied sciences
Automation
Computer science; control theory; systems
Control system analysis
Control theory. Systems
Exact sciences and technology
Inertia
Linear and multilinear algebra, matrix theory
Mathematical analysis
Mathematics
Nonnegative semidefinite matrix
Rank
Sciences and techniques of general use
Sylvester equation
Nonnegative semidefinite matrix
Rank
Inertia
Sylvester equation
Non negative matrix
Operator equation
Necessary and sufficient condition
Hermite interpolation
Matrix equation
Solvability
Semidefinite matrix
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Summary:In this paper, we give some necessary and sufficient solvability conditions for the mixed Sylvester matrix equations, and parameterize general solution when it is solvable. Moreover, we investigate the maximal and minimal ranks of the general solution, and maximal and minimal ranks and inertias of Hermitian part of solution, respectively.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2013.06.009