The well-known Generalized Champagne Problem on simultaneous stabilization of linear systems is solved by using complex analysis and Blonders technique. We give a complete answer to the open problem proposed by Patel ...The well-known Generalized Champagne Problem on simultaneous stabilization of linear systems is solved by using complex analysis and Blonders 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.展开更多
Simultaneous stabilization of linear systems is a fundamental issue in the system and control theory, and is of theoretical and practical significance. In this paper, the authors review the recent research progress an...Simultaneous stabilization of linear systems is a fundamental issue in the system and control theory, and is of theoretical and practical significance. In this paper, the authors review the recent research progress and the state-of-art results on simultaneous stabilization of single-input single-output linear time-invariant systems. Especially, the authors list the ever best results on the parameters involved in the well known ＂French Champagne Problem＂ and ＂Belgian Chocolate Problem＂ from the point of view of mathematical theoretical analysis and numerical calculation. And the authors observed that Boston claimed the lower bound of 5 can be enlarged to 0.976461 in 2012 is not accurate. The authors hope it will inspire further study on simultaneous stabilization of several linear systems.展开更多
基金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)+1 种基金the Overseas Outstanding Young Researcher Foundation of Chinese Academy of Sciencesthe Program of National Key Laboratory of Intelligent Technology and Systems of Tsinghua University
文摘The well-known Generalized Champagne Problem on simultaneous stabilization of linear systems is solved by using complex analysis and Blonders 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.
基金supported by the National Natural Science Foundation under Grant Nos.61370176 and 61571064
文摘Simultaneous stabilization of linear systems is a fundamental issue in the system and control theory, and is of theoretical and practical significance. In this paper, the authors review the recent research progress and the state-of-art results on simultaneous stabilization of single-input single-output linear time-invariant systems. Especially, the authors list the ever best results on the parameters involved in the well known ＂French Champagne Problem＂ and ＂Belgian Chocolate Problem＂ from the point of view of mathematical theoretical analysis and numerical calculation. And the authors observed that Boston claimed the lower bound of 5 can be enlarged to 0.976461 in 2012 is not accurate. The authors hope it will inspire further study on simultaneous stabilization of several linear systems.
