| 关于Lyapunov稳定性若干定理的推广 |
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| 引用本文： | 高莲,包曙红.关于Lyapunov稳定性若干定理的推广[J].内蒙古师范大学学报(自然科学版),2006,35(4):407-412. |
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| 作者姓名： | 高莲 包曙红 |
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| 作者单位： | [1]内蒙古农业大学理学院,内蒙古呼和浩特010018 [2]内蒙古工业大学电力学院,内蒙古呼和浩特010080 |
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| 基金项目： | 致谢感谢导师斯力更教授的悉心指导! |
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| 摘 要： | 利用两个推广的积分不等式．对Lyapunov函数中的限制条件做了改进，得到非自治矢量微分方程零解的稳定性、渐近稳定性及一致稳定性的充分性定理，推广了扰动微分方程组零解稳定性的若干判定定理．
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| 关 键 词： | Lyapunov函数 稳定 渐近稳定 一致稳定 |
| 文章编号： | 1001-8735（2006）04-0407-06 |
| 收稿时间： | 2006-03-20 |
| 修稿时间： | 2006年3月20日 |
The Generalization of Theorems about Lyapunov Stability Theory |
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| GAO Lian,BAO Shu-hong.The Generalization of Theorems about Lyapunov Stability Theory[J].Journal of Inner Mongolia Normal University(Natural Science Edition),2006,35(4):407-412. |
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| Authors: | GAO Lian BAO Shu-hong |
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| Institution: | 1. College of Science, Inner Mongolia Agricultural University, Huhhot 010018 ,China ; 2. College of Electricity, Inner Mongolia Industrial University, Huhhot 010080 ,China |
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| Abstract: | By using two generalized integral inequalities,the limitation conditions of Lyapunov function were improved. Sufficient theorems of stability, asymptotic stability and uniformly stability for zero solution of the non-autonomous vector differential equation were obtained, and certain criteria theorems of the disturbing differential equations were extended. |
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| Keywords: | Lyapunov function stability asymptotic stability uniformly stability |
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