Parameterized solution to a class of sylvester matrix equations

Authors:
Yu-Peng Qiao;Hong-Sheng Qi;Dai-Zhan Cheng
Affiliations:
Center for Control and Optimization, College of Automation Science and Engineering, South China University of Technology, Guangzhou, PRC 510641;Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, PRC 100190;Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, PRC 100190
Venue:
International Journal of Automation and Computing
Year:
2010

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Abstract

A class of formulas for converting linear matrix mappings into conventional linear mappings are presented. Using them, an easily computable numerical method for complete parameterized solutions of the Sylvester matrix equation AX 驴 EXF = BY and its dual equation XA 驴 FXE = Y C are provided. It is also shown that the results obtained can be used easily for observer design. The method proposed in this paper is universally applicable to linear matrix equations.