Solvability conditions and general solution for mixed Sylvester equations

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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Veröffentlicht in:Automatica (Oxford) 2013-09, Vol.49 (9), p.2713-2719
Hauptverfasser: Wang, Qing-Wen, He, Zhuo-Heng
Format: Artikel
Sprache:eng
Schlagworte:
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
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Beschreibung
Zusammenfassung: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2013.06.009