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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| Published in | Automatica (Oxford) Vol. 49; no. 9; pp. 2713 - 2719 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Kidlington
Elsevier Ltd
01.09.2013
Elsevier |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Wang, Qing-Wen He, Zhuo-Heng |
| Author_xml | – sequence: 1 givenname: Qing-Wen surname: Wang fullname: Wang, Qing-Wen email: wqw369@yahoo.com – sequence: 2 givenname: Zhuo-Heng surname: He fullname: He, Zhuo-Heng email: hzh19871126@126.com |
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| Cites_doi | 10.1109/CACSD.2000.900179 10.1016/j.camwa.2011.07.029 10.1109/TAC.2006.874989 10.1016/0024-3795(79)90004-1 10.1016/j.automatica.2010.10.038 10.1080/03081080008818664 10.1137/S0895479802415545 10.1109/TAC.1987.1104702 10.1109/TNN.2002.1031938 10.1137/S0363012904441350 10.1137/S0895479898346983 10.1016/j.camwa.2006.05.011 10.1016/j.sysconle.2004.07.002 10.1080/03081087408817070 10.1002/oca.4660040302 10.1109/9.284883 10.1016/j.laa.2012.06.004 |
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| Keywords | 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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| SubjectTerms | 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 |
| Title | Solvability conditions and general solution for mixed Sylvester equations |
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