| 离散动态系统稳定与不稳定的简捷判据 |
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| 引用本文： | 韩金舫,王清印,李永伟. 离散动态系统稳定与不稳定的简捷判据[J]. 系统工程与电子技术, 2004, 26(9): 1254-1256 |
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| 作者姓名： | 韩金舫 王清印 李永伟 |
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| 作者单位： | 1. 河北科技大学工程数学研究所,河北,石家庄,050054
2. 河北经贸大学不确定性系统科学研究所,河北,石家庄,050091 |
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| 基金项目： | 国家自然科学基金(70271006)，河北省教育厅科研基金(2003305)资助课题 |
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| 摘 要： | 运用矩阵特征值分析技巧研究了区间矩阵及一类离散动态系统的稳定性问题。在无需任何附加条件的情况下,仅用区间矩阵的界阵元素给出了一般区间矩阵及离散动态系统混合稳定、渐进(离散)稳定与不稳定的简便代数判据(含充分条件、必要条件与充要条件),弃掉了对区间矩阵的下(上)界阵为非负(正)的条件要求。相对于现存结果,提出判据不仅明显具有普适性强实用范围广且保守性小的特性,而且还涵盖了一些原有的稳定性判据。
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| 关 键 词： | 离散动态系统 渐近稳定性 特征值分析 区间矩阵 离散稳定 混合稳定 |
| 文章编号： | 1001-506X(2004)09-1254-03 |
| 修稿时间： | 2003-07-01 |
Simple criteria for stability and instability of discrete dynamic systems |
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| HAN Jin-fang,WANG Qing-yin,Li Yong-wei. Simple criteria for stability and instability of discrete dynamic systems[J]. System Engineering and Electronics, 2004, 26(9): 1254-1256 |
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| Authors: | HAN Jin-fang WANG Qing-yin Li Yong-wei |
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| Affiliation: | HAN Jin-fang~1,WANG Qing-yin~2,Li Yong-wei~1 |
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| Abstract: | The stability problems of interval matrices and a class of discrete dynamic systems are investigated by means of the analysis technique of matric eigenvalues. Several simple and practical algebraic criteria (including sufficient conditions, necessary conditions, and necessary and sufficient conditions), for the mixed stability, asymptotic (discretely) stability and instability of interval matrices and discrete dynamic systems, are obtained, which use only the entries of boundary matrix of the interval matrices. That the conditions of lower (upper) boundary matrix being nonnegtive (nonpositive) in the previous literatures are abandoned. The proposed results are wider applicable and less conservative than existing criteria, and some of them are inclusive of the previous results of stability. |
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| Keywords: | discrete dynamic systems asymptotic stability eigenvalues analysis interval matrices discretely stability mixed stability |
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