Polynomial Solutions to the Matrix Equation X−AXTB=C
Solutions are constructed for the Kalman-Yakubovich-transpose equation X−AXTB=C. The solutions are stated as a polynomial of parameters of the matrix equation. One of the polynomial solutions is expressed by the symmetric operator matrix, controllability matrix, and observability matrix. Moreover, t...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/710458 |
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| _version_ | 1832548104779333632 |
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| author | Caiqin Song Jun-e Feng |
| author_facet | Caiqin Song Jun-e Feng |
| author_sort | Caiqin Song |
| collection | DOAJ |
| description | Solutions are constructed for the Kalman-Yakubovich-transpose equation X−AXTB=C. The solutions are stated as a polynomial of parameters of the matrix equation. One of the polynomial solutions is expressed by the symmetric operator matrix, controllability matrix, and observability matrix. Moreover, the explicit solution is proposed when the Kalman-Yakubovich-transpose matrix equation has a unique solution. The provided approach does not require the coefficient matrices to be in canonical form. In addition, the numerical example is given to illustrate the effectiveness of the derived method. Some applications in control theory are discussed at the end of this paper. |
| format | Article |
| id | doaj-art-2522619321af422880e0013f434428b0 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2522619321af422880e0013f434428b02025-02-03T06:42:12ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/710458710458Polynomial Solutions to the Matrix Equation X−AXTB=CCaiqin Song0Jun-e Feng1School of Mathematics, Shandong University, Jinan 250100, ChinaSchool of Mathematics, Shandong University, Jinan 250100, ChinaSolutions are constructed for the Kalman-Yakubovich-transpose equation X−AXTB=C. The solutions are stated as a polynomial of parameters of the matrix equation. One of the polynomial solutions is expressed by the symmetric operator matrix, controllability matrix, and observability matrix. Moreover, the explicit solution is proposed when the Kalman-Yakubovich-transpose matrix equation has a unique solution. The provided approach does not require the coefficient matrices to be in canonical form. In addition, the numerical example is given to illustrate the effectiveness of the derived method. Some applications in control theory are discussed at the end of this paper.http://dx.doi.org/10.1155/2014/710458 |
| spellingShingle | Caiqin Song Jun-e Feng Polynomial Solutions to the Matrix Equation X−AXTB=C Journal of Applied Mathematics |
| title | Polynomial Solutions to the Matrix Equation X−AXTB=C |
| title_full | Polynomial Solutions to the Matrix Equation X−AXTB=C |
| title_fullStr | Polynomial Solutions to the Matrix Equation X−AXTB=C |
| title_full_unstemmed | Polynomial Solutions to the Matrix Equation X−AXTB=C |
| title_short | Polynomial Solutions to the Matrix Equation X−AXTB=C |
| title_sort | polynomial solutions to the matrix equation x axtb c |
| url | http://dx.doi.org/10.1155/2014/710458 |
| work_keys_str_mv | AT caiqinsong polynomialsolutionstothematrixequationxaxtbc AT junefeng polynomialsolutionstothematrixequationxaxtbc |