| 一类稳定矩阵的共同二次李雅谱诺夫函数的构造 |
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| 引用本文： | 朱亚红, 程代展, 秦化淑. 一类稳定矩阵的共同二次李雅谱诺夫函数的构造. 自动化学报, 2007, 33(2): 202-204. doi: 10.1360/aas-007-0202 |
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| 作者姓名： | 朱亚红 程代展 秦化淑 |
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| 作者单位： | 1.中科院数学与系统科学研究院，北京 100080 |
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| 摘 要： | Nerendra 和 Balakrishnan对一组两两可交换的稳定矩阵提出了计算其共同二次李雅谱诺夫函数的方法。本文修改了此方法，并运用于一组两两不可交换的稳定矩阵的共同二次李雅谱诺夫函数的计算。
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| 关 键 词： | 切换系统 共同二次李雅谱诺夫函数 李代数 |
| 收稿时间： | 2005-09-14 |
| 修稿时间： | 2006-09-19 |
Constructing Common Quadratic Lyapunov Functions for a Class of Stable Matrices |
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| ZHU Ya-Hong, CHENG Dai-Zhan, QIN Hua-Shu. Constructing Common Quadratic Lyapunov Functions for a Class of Stable Matrices. ACTA AUTOMATICA SINICA, 2007, 33(2): 202-204. doi: 10.1360/aas-007-0202 |
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| Authors: | ZHU Ya-Hong CHENG Dai-Zhan QIN Hua-Shu |
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| Affiliation: | 1. Institute of Systems Science, Chinese Academy of Sciences, Beijing 100080 |
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| Abstract: | Narendra and Balakrishnan proposed a way to construct a common quadratic Lyapunov function (CQLF), when a set of stable matrices are commutative. The purpose of this paper is to generalize the method to non-commutative and non-solvable case. A modified constructing algorithm is proposed and certain conditions are provided to assure the resulting matrix being a CQLF. Next, the problem discussed is when a stable matrix can be added to a set of matrices with CQLF to construct a new CQLF for the enlarged set. |
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| Keywords: | Switched system common quadratic Lyapunov function Lie algebra |
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