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| 具有临界和非临界操作错误的人机系统的渐近稳定性 | |
| 引用本文： | 徐厚宝,柳合龙,于景元,朱广田.具有临界和非临界操作错误的人机系统的渐近稳定性[J].系统科学与数学,2005,25(5):513-524. |
| 作者姓名： | 徐厚宝 柳合龙 于景元 朱广田 |
| 作者单位： | 1. 北京理工大学应用数学系,北京,100081;北京信息控制研究所,北京,100037 2. 信阳师范学院数学系,信阳,464000 3. 北京信息控制研究所,北京,100037 4. 中科院数学与系统科学研究院,北京,100080 |
| 摘 要： | 讨论具有临界和非临界操作错误的可修复人机系统．利用系统算子生成的Banach 空间中的正压缩C0半群的性质,证明了此系统的唯一非负时间依赖解恰是系统算子0本征值对应的规范化后的本征向量;同时通过对系统算子谱点分布情况的分析,证明了系统算子的谱点均位于复平面左半平面且在虚轴上除0点外无其它谱,作为线性算子半群稳定性的一个直接结果,得出了该可修人机系统的渐近稳定性． |
| 关 键 词： | 人机系统 C0半群 渐近稳定 |
| 修稿时间： | 2003年12月20 |
THE ASYMPTOTIC STABILITY OF A MAN-MACHINE SYSTEM WITH CRITICAL AND NON-CRITICAL HUMAN ERROR |
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| Xu Houbao,Liu Helong,Yu Jingyuan,Zhu Guangtian.THE ASYMPTOTIC STABILITY OF A MAN-MACHINE SYSTEM WITH CRITICAL AND NON-CRITICAL HUMAN ERROR[J].Journal of Systems Science and Mathematical Sciences,2005,25(5):513-524. | |
| Authors: | Xu Houbao Liu Helong Yu Jingyuan Zhu Guangtian |
| Institution: | (1)Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081;Beijing Institute of Information and Control, Beijing 100037;(2)Department of Mathematics, Xinyang Teachers college,Xinyang 464000;(3)Beijing Institute of Information and Control, Beijing 10003 |
| Abstract: | This paper presents the asymptotic stability of a human-machine system associated with critical and non-critical human errors. We show that the system operator generates a positive C0-semigroup in the state Banach space. The steady-state solution is shown to be the eigenvector of system operator corresponding to the eigenvalue 0. By analyzing the spectrum of the system operator, we find that 0 is the unique spectral point of the system operator on the imaginary axis. As a result, the asymptotic stability of the system is obtained. |
| Keywords: | Human-machine system C0 semi-group asymptotic stability |
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