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| Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems | |
| 作者单位： | GUAN Qiang（Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China） ;WANG Long（Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China） ;XIA BiCan（LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China） ;YANG Lu（Shanghai Institute of Theoretical Computing, Software Engineering Institute, East China Normal University, Shanghai 200062, China） ;YU WenSheng（Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China;National Key Laboratory of Intelligent Technology and Systems, Tsinghua University, Beijing 100084, China） ;ZENG ZhenBing（Shanghai Institute of Theoretical Computing, Software Engineering Institute, East China Normal University, Shanghai 200062, China） ; |
| 基金项目： | 国家自然科学基金;国家重点基础研究发展计划(973计划) |
| 摘 要： | 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 auto-matically includes the solution to the original Champagne Problem. Based on the recent development in automated inequality-type theorem proving, a new stabiliz-ing controller design method is established. Our numerical examples significantly improve the relevant results in the literature. |
| 收稿时间： | 2007-02-26 |
| 修稿时间： | 2007-04-18 |
Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems |
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| Guan Qiang,Wang Long,Xia BiCan,Yang Lu,Yu WenSheng,Zeng ZhenBing. Solution to the Generalized Champagne Problem on simultaneous stabilization of linear systems[J]. Science in China(Information Sciences), 2007, 50(5): 719-731. DOI: 10.1007/s11432-007-0053-2 | |
| Authors: | Guan Qiang Wang Long Xia BiCan Yang Lu Yu WenSheng Zeng ZhenBing |
| Affiliation: | 1. Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China 2. Center for Systems and Control, College of Engineering, Peking University, Beijing 100871, China 3. LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China 4. Shanghai Institute of Theoretical Computing, Software Engineering Institute, East China Normal University, Shanghai 200062, China 5. Laboratory of Complex Systems and Intelligence Science, Institute of Automation, Chinese Academy of Sciences, Beijing 100080, China;National Key Laboratory of Intelligent Technology and Systems, Tsinghua University, Beijing 100084, China |
| 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. 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 |
| Keywords: | linear systems stabilization simultaneous stabilization Champagne Problem Generalized Champagne Problem complex analysis inequality-type theorem automated theorem proving |
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