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Parameterized solution to a class of sylvester matrix equations

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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 − EXF = BY and its dual equation XA − 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.

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Authors and Affiliations

  1. Center for Control and Optimization, College of Automation Science and Engineering, South China University of Technology, Guangzhou, 510641, PRC

    Yu-Peng Qiao

  2. Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, PRC

    Hong-Sheng Qi & Dai-Zhan Cheng

Authors
  1. Yu-Peng Qiao
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  2. Hong-Sheng Qi
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  3. Dai-Zhan Cheng
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Corresponding author

Correspondence to Yu-Peng Qiao.

Additional information

This work was supported by National Natural Science Foundation of China (No. 60736022, No. 60821091).

Yu-Peng Qiao graduated from Harbin Institute of Technology (HIT), PRC in 2003. She received the M. Sc. degree from HIT in 2005 and the Ph.D. degree from Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PRC in 2008. She is currently a post-doctoral fellow at the Center for Control and Optimization, College of Automation Science and Engineering, South China University of Technology, PRC.

Her research interests include nonlinear system control, guidance problem, and switched systems.

Hong-Sheng Qi received the Ph.D. degree in systems theory from Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PRC in 2008. He is currently a post-doctoral fellow at the Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences.

His research interests include nonlinear control and systems biology.

Dai-Zhan Cheng received the Ph.D. degree from Washington University, St. Louis, USA in 1985. He is currently a professor with Academy of Mathematics and Systems Science, Chinese Academy of Sciences, PRC. He is a chairman of Technical Committee on Control Theory, Chinese Association of Automation and a fellow of IEEE and IFAC.

His research interests include nonlinear systems, numerical method, switched systems, and systems biology.

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Qiao, YP., Qi, HS. & Cheng, DZ. Parameterized solution to a class of sylvester matrix equations. Int. J. Autom. Comput. 7, 479–483 (2010). https://doi.org/10.1007/s11633-010-0530-8

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  • DOI: https://doi.org/10.1007/s11633-010-0530-8

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