| 引用本文: | 关强,何冠男,王龙,郁文生.线性系统的同时镇定问题[J].控制理论与应用,2011,28(1):1~12.[点击复制] |
| GUAN Qiang,HE Guan-nan,WANG Long,YU Wen-sheng.Simultaneous stabilization of linear systems[J].Control Theory and Technology,2011,28(1):1~12.[点击复制] |
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| 线性系统的同时镇定问题 |
| Simultaneous stabilization of linear systems |
| 摘要点击 3149 全文点击 3391 投稿时间：2010-04-13 修订日期：2010-07-05 |
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| DOI编号 10.7641/j.issn.1000-8152.2011.1.CCTA100396 |
| 2011,28(1):1-12 |
| 中文关键词 线性系统 同时镇定 香槟问题 比利时巧克力问题 威士忌问题 复分析 不等式型定理 机器证明 半代数系统 |
| 英文关键词 linear systems simultaneous stabilization champagne problem Belgian chocolate problem Whiskey problem complex analysis inequality-type theorem automated theorem proving semi-algebraic systems |
| 基金项目 国家自然科学基金资助项目(61070048, 60874010); 国家自然科学基金委员会创新研究群体科学基金资助项目(61021004); 国家重点基础研究发展规划资助项目(2011CB302802); 上海市教育委员会科研创新资助项目(11ZZ37). |
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| 中文摘要 |
| 线性系统的同时镇定问题, 是系统与控制理论中的基本问题, 有着广泛的理论意义和应用价值. 本文介绍了线性系统同时镇定问题的研究现状和最新进展. 首先回顾了同时镇定问题的研究内容、基本方法及相关结果. 其次, 从理论求解和控制器设计的角度对线性系统同时镇定研究中著名的“香槟问题”,“比利时巧克力问题”和“威士忌问题”进行了分析探讨, 并基于不等式型定理机器证明理论, 给出了线性系统同时镇定问题的相关工作. 最后指出了对于同时镇定多个线性系统方面的若干研究方向. |
| 英文摘要 |
| Simultaneous stabilization of linear systems is a fundamental issue in system and control theory, and is of theoretical, as well as practical, significance. Current theories and recent developments in the simultaneous stabilization of linear systems are discussed. Firstly, the substance of the simultaneous stabilization of linear systems, the basic research methods and the related results are reviewed. Some well-known problems, including the“champagne problem”, “Belgian chocolate problem” and “Whiskey problem” are analyzed from the perspectives of theoretical solution and controller design. Based on the development in automated inequality-type theorem proving, some original work on solving these open problems is also presented. Finally, possible future research directions for the simultaneous stabilization of linear systems are given. |
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