Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 60, Issue 1, Pages 95-111Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2010.04.035
Keywords
Sylvester-conjugate equation; Closed-form solution; Parametric expression; Controllability matrix; Observability matrix
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Funding
- Research Grants Council of The Hong Kong Special Administrative Region [113708]
- National Natural Science Foundation of China [60974044, 60710002]
- Fundamental Research Funds for the Central Universities [HIT.NSRIF.2009137]
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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. (C) 2010 Elsevier Ltd. All rights reserved.
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