Closed-form solutions to Sylvester-conjugate matrix equations

Authors:
Ai-Guo Wu;Gang Feng;Guang-Ren Duan;Wei-Jun Wu
Affiliations:
Information and Control Research Center, Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, PR China and Department of Manufacturing Engineering and Engineering Management, ...;Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong;Center for Control Theory and Guidance Technology, Harbin Institute of Technology, P. O. Box 416, Harbin 150001, PR China and Information and Control Research Center, Harbin Institute of Technolog ...;National Key Laboratory of Antennas and Microwave Technology, Xidian University, Xi'an, PR China
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

Some explicit closed-form solutions of homogeneous and nonhomogeneous Sylvester-conjugate 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 Sylvester-conjugate equation, some new expressions of the solutions of the normal Sylvester, normal Sylvester-conjugate and Sylvester equations are given. This fact reveals that the Sylveter-conjugate matrix equations are a more general class of some previously investigated matrix equations.