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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 2356-6140 1537-744X |