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The Scientific World Journal
Volume 2014, Article ID 543610, 7 pages
http://dx.doi.org/10.1155/2014/543610
Research Article

A New Solution to the Matrix Equation

School of Mathematical Sciences, University of Jinan, Jinan 250022, China

Received 16 April 2014; Accepted 28 June 2014; Published 15 July 2014

Academic Editor: Kaleem R. Kazmi

Copyright © 2014 Caiqin Song. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the matrix equation . For convenience, the matrix equation 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.