On solutions to the matrix equations XB−AX=CY and XB−AX^=CY. Issue 5 (March 2016)

• Record Type: Journal Article
• Authors: Song, Caiqin; Feng, Jun-e
• Is Part Of: Journal of the Franklin Institute. Volume 353:Issue 5(2016:Mar.)
• Page Start: 1075
• Page End: 1088
• Publication Date: 2016-03
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2015.04.009
• Languages: English
• ISSNs: 0016-0032

Abstract

Abstract: The solution of the generalized Sylvester real matrix equation XB − AX = CY is important in stability analysis and controller design in linear systems. This paper presents an explicit solution to the generalized Sylvester real matrix equation XB − AX = CY . Based on the derived explicit solution to the considered generalized Sylvester real matrix equation, a new approach is provided for obtaining the solutions to the generalized Sylvester quaternion j-conjugate matrix equation XB − A X ^ = CY using the real representation of a quaternion matrix. The closed form solution is established in an explicit form for this generalized Sylvester quaternion j-conjugate matrix equation. The existing complex representation method requires the coefficient matrix A to be a block diagonal matrix over complex field, while it is any suitable dimension quaternion matrix in the present paper. Therefore, we generalize the existing results.