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Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems

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Abstract

The well-known Generalized Champagne Problem on simultaneous stabilization of linear systems is solved by using complex analysis and Blondel’s technique. We give a complete answer to the open problem proposed by Patel et al., which automatically includes the solution to the original Champagne Problem. Based on the recent development in automated inequality-type theorem proving, a new stabilizing controller design method is established. Our numerical examples significantly improve the relevant results in the literature.

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Authors and Affiliations

  1. Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing, 100080, China

    Guan Qiang & Yu WenSheng

  2. Center for Systems and Control, College of Engineering, Peking University, Beijing, 100871, China

    Wang Long

  3. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, China

    Xia BiCan

  4. Shanghai Institute of Theoretical Computing, Software Engineering Institute, East China Normal University, Shanghai, 200062, China

    Yang Lu & Zeng ZhenBing

  5. National Key Laboratory of Intelligent Technology and Systems, Tsinghua University, Beijing, 100084, China

    Yu WenSheng

Authors
  1. Guan Qiang
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  2. Wang Long
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  3. Xia BiCan
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  4. Yang Lu
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  5. Yu WenSheng
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  6. Zeng ZhenBing
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Corresponding author

Correspondence to Yu WenSheng.

Additional information

Supported by the National Natural Science Foundation of China (Grant Nos. 60572056, 60528007, 60334020, 60204006, 10471044, and 10372002), the National Key Basic Research and Development Program (Grant Nos. 2005CB321902, 2004CB318003, 2002CB312200), the Overseas Outstanding Young Researcher Foundation of Chinese Academy of Sciences and the Program of National Key Laboratory of Intelligent Technology and Systems of Tsinghua University

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Guan, Q., Wang, L., Xia, B. et al. Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems. SCI CHINA SER F 50, 719–731 (2007). https://doi.org/10.1007/s11432-007-0053-2

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  • DOI: https://doi.org/10.1007/s11432-007-0053-2

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