A New Solution to the Matrix Equation X−AX¯B=C. (15th July 2014)

• Record Type: Journal Article
• Authors: Song, Caiqin
• Other Names: Kazmi Kaleem R. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-07-15
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/543610
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : We investigate the matrix equation X − A X ¯ B = C . For convenience, the matrix equation X − A X ¯ 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.