Closed-form solutions to Sylvester-conjugate matrix equations

✍ Scribed by Ai-Guo Wu; Gang Feng; Guang-Ren Duan; Wei-Jun Wu

• Publisher: Elsevier Science
• Year: 2010
• Tongue: English
• Weight: 472 KB
• Volume: 60
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2010.04.035

✦ Synopsis

Some explicit closed-form solutions of homogeneous and nonhomogeneous Sylvesterconjugate matrix equations are provided in this paper. One of the solutions is expressed in terms of controllability matrices and observability matrices. The proposed approach does not require all the coefficient matrices to be in any canonical forms and the solutions provide a significant degree of freedom which is represented by an arbitrarily chosen parameter matrix. By specifying the solutions of the homogeneous Sylvesterconjugate equation, some new expressions of the solutions of the normal Sylvester, normal Sylvester-conjugate and Sylvester equations are given. This fact reveals that the Sylveterconjugate matrix equations are a more general class of some previously investigated matrix equations.