The complete solution to the Sylvester-polynomial-conjugate matrix equations

Authors:
Ai-Guo Wu;Gang Feng;Wanquan Liu;Guang-Ren Duan
Affiliations:
Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, PR China;Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, Kowloon, Hong Kong;Department of Computing, Curtin University of Technology, Perth WA 6102, Australia;Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin 150001, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2011

Citing 5
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Abstract

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.