A New Solution to the Matrix Equation X−AX¯B=C
We investigate the matrix equation X−AX¯B=C. For convenience, the matrix equation X−AX¯B=C is named as Kalman-Yakubovich-conjugate matrix equation. The explicit solution is constructed when the above matrix equation has unique solution. And this solution is stated as a polynomial of coefficient matr...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/543610 |
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| author | Caiqin Song |
| author_facet | Caiqin Song |
| author_sort | Caiqin Song |
| collection | DOAJ |
| description | We investigate the matrix equation X−AX¯B=C. For convenience, the matrix equation X−AX¯B=C is named as Kalman-Yakubovich-conjugate matrix equation. The explicit
solution is constructed when the above matrix equation has unique solution. And this solution is
stated as a polynomial of coefficient matrices of the matrix equation. Moreover, the explicit solution
is also expressed by the symmetric operator matrix, controllability matrix, and observability matrix.
The proposed approach does not require the coefficient matrices to be in arbitrary canonical form.
At the end of this paper, the numerical example is shown to illustrate the effectiveness of the
proposed method. |
| format | Article |
| id | doaj-art-cfb0f6fbabfb46b7b85b26dc8700ec5d |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-cfb0f6fbabfb46b7b85b26dc8700ec5d2025-02-03T01:10:18ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/543610543610A New Solution to the Matrix Equation X−AX¯B=CCaiqin Song0School of Mathematical Sciences, University of Jinan, Jinan 250022, ChinaWe investigate the matrix equation X−AX¯B=C. For convenience, the matrix equation X−AX¯B=C is named as Kalman-Yakubovich-conjugate matrix equation. The explicit solution is constructed when the above matrix equation has unique solution. And this solution is stated as a polynomial of coefficient matrices of the matrix equation. Moreover, the explicit solution is also expressed by the symmetric operator matrix, controllability matrix, and observability matrix. The proposed approach does not require the coefficient matrices to be in arbitrary canonical form. At the end of this paper, the numerical example is shown to illustrate the effectiveness of the proposed method.http://dx.doi.org/10.1155/2014/543610 |
| spellingShingle | Caiqin Song A New Solution to the Matrix Equation X−AX¯B=C The Scientific World Journal |
| title | A New Solution to the Matrix Equation X−AX¯B=C |
| title_full | A New Solution to the Matrix Equation X−AX¯B=C |
| title_fullStr | A New Solution to the Matrix Equation X−AX¯B=C |
| title_full_unstemmed | A New Solution to the Matrix Equation X−AX¯B=C |
| title_short | A New Solution to the Matrix Equation X−AX¯B=C |
| title_sort | new solution to the matrix equation x ax¯b c |
| url | http://dx.doi.org/10.1155/2014/543610 |
| work_keys_str_mv | AT caiqinsong anewsolutiontothematrixequationxaxbc AT caiqinsong newsolutiontothematrixequationxaxbc |