| 输入矩阵定常型切换线性系统的能控性探讨 |
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| 引用本文： | 徐志宇,许维胜,吴启迪.输入矩阵定常型切换线性系统的能控性探讨[J].同济大学学报(自然科学版),2010,38(4):586-588. |
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| 作者姓名： | 徐志宇 许维胜 吴启迪 |
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| 作者单位： | 同济大学,电子与信息工程学院,上海,201804 |
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| 基金项目： | 国家"八六三"高技术研究发展计划资助项目 |
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| 摘 要： | 重新考察一类切换线性系统的能控性,这类系统具有不同的系统矩阵和相同的输入矩阵.研究发现文献导出的必要充分条件为假命题,该判据只适用于2阶系统,对于3阶及以上系统其必要性不一定成立.并证明第一不变子空间只是能控状态集的真子集,而非其全体.最后通过1个反例对结论予以验证.
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| 关 键 词： | 切换线性系统 输入矩阵定常 能控性 能控状态集 必要充分条件 |
| 收稿时间： | 2/25/2009 7:53:07 PM |
| 修稿时间： | 2010/1/25 0:00:00 |
Discussion on Controllability of Switched Linear System with Constant Input Matrix |
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| XU Zhi-yu,XU Wei-sheng and WU Qi-di.Discussion on Controllability of Switched Linear System with Constant Input Matrix[J].Journal of Tongji University(Natural Science),2010,38(4):586-588. |
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| Authors: | XU Zhi-yu XU Wei-sheng and WU Qi-di |
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| Institution: | School of electronics and information engineering, Tongji University,School of electronics and information engineering, Tongji University,School of electronics and information engineering, Tongji University |
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| Abstract: | This paper re-examines the controllability of a class of switched linear systems which has different systematic matrices and the same input matrix. Investigations reveal that the necessary and sufficient condition derived in literatures is a false proposition: it only holds for second-order systems, while the necessity is not always true for systems of third and higher order. We also prove that the first invariant subspace is a proper subset of controllable state set rather than the whole of it. Finally, a counterexample is presented to illustrate the conclusion. |
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| Keywords: | switched linear system constant input matrix controllability controllable state set necessary and sufficient condition |
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