| 线性切换系统的非奇异变换 |
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| 引用本文： | 谢广明,郑大钟.线性切换系统的非奇异变换[J].清华大学学报(自然科学版),2002,42(9):1273-1275. |
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| 作者姓名： | 谢广明 郑大钟 |
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| 作者单位： | 清华大学,自动化系,北京,100084 |
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| 基金项目： | 国家自然科学基金资助项目 (60 0 740 12 )，攀登计划预研项目 (970 2 110 17)，国家“九七三”基础研究基金项目(G19980 2 0 3 0 5 )，清华大学“九八五”基础研究基金资助项目 |
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| 摘 要： | 线性切换系统是一类重要的混合动态系统。为了深入分析线性切换系统的能控性 ,寻找系统能控性判定的充要条件 ,首次研究了线性切换系统在非奇异变换下的性质。首先 ,证明线性切换系统的能控性在任意非奇异变换下保持不变。其次 ,基于一个恰当的非奇异变换 ,将状态空间适当分解为两个部分 ,给出了一个能控性的必要性条件的新证明。该证明比之已有证明更加简洁直观。最后 ,通过一个具体例 ,验证了能控性在非奇异变换下确实不变。
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| 关 键 词： | 线性切换系统 混合动态系统 非奇异变换 能控性 不变性 |
| 文章编号： | 1000-0054(2002)09-1273-03 |
| 修稿时间： | 2001年5月18日 |
Nonsingular transformation of linear switched systems |
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| XIE Guangming,ZHENG Dazhong.Nonsingular transformation of linear switched systems[J].Journal of Tsinghua University(Science and Technology),2002,42(9):1273-1275. |
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| Authors: | XIE Guangming ZHENG Dazhong |
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| Abstract: | Linear switched systems are an important class of hybrid dynamic systems. The controllability of linear switched systems and the necessary and sufficient criteria for the controllability of linear switched systems were studied by analyzing the performance of linear switched systems using nonsingular transformations. The controllability of linear switched systems was found to be invariant for any nonsingular transformation. Then, with the proper nonsingular transformation, the system state space could be decomposed into two parts which gave a new proof for a necessary condition for controllability of linear switched systems. Finally, an example is given to verify that the controllability is not changed by any nonsingular transformation. |
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| Keywords: | linear switched systems hybrid dynamic systems nonsingular transformation controllability invariance |
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