Journal
MATHEMATICAL AND COMPUTER MODELLING
Volume 53, Issue 9-10, Pages 2044-2056Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.mcm.2010.12.038
Keywords
Conjugate product; Sylvester-conjugate sum; Sylvester-polynomial-conjugate matrix equations; Complete solution
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Funding
- National Natural Science Foundation of China [60974044]
- Research Grants Council of The Hong Kong Special Administrative Region [CityU 113708]
- Fundamental Research Funds for the Central Universities [HIT.NSRIF.2009137]
- Natural Science Foundation of Guangdong Province [10451805707004154]
- Basic Research Plan in Shenzhen City [JC200903120195A]
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In this paper we propose two new operators for complex polynomial matrices. One is the conjugate product and the other is the Sylvester-conjugate sum. Then some important properties for these operators are proved. Based on these derived results, we propose a unified approach to solving a general class of Sylvester-polynomial-conjugate matrix equations, which include the Yakubovich-conjugate matrix equation as a special case. The complete solution of the Sylvester-polynomial-conjugate matrix equation is obtained in terms of the Sylvester-conjugate sum, and such a proposed solution can provide all the degrees of freedom with an arbitrarily chosen parameter matrix. (C) 2010 Elsevier Ltd. All rights reserved.
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