| 泛函微分系统依照两个测度的稳定性 |
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| 引用本文： | 刘开恩,杨国为.泛函微分系统依照两个测度的稳定性[J].青岛大学学报(自然科学版),2008,21(1):11-17. |
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| 作者姓名： | 刘开恩 杨国为 |
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| 作者单位： | 1. 青岛大学数学科学学院,山东,青岛,266071
2. 青岛大学自动化工程学院,山东,青岛,266071 |
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| 基金项目： | 国家自然科学基金
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山东省自然科学基金
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青岛大学校科研和教改项目 |
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| 摘 要： | 运用变分Lyapunov方法，研究了泛函微分系统依照两个测度的稳定性。首先，给出了关于微分系统的一个Razumikhin型比较定理。进一步，得到一个变分比较定理。根据此结果，在未扰动系统为常微分系统的情形下，建立了关于泛函微分系统依照两个测度稳定性的判定定理，推广并改进了已有结果。
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| 关 键 词： | 泛函微分系统 两个测度的稳定性 变分Lyapunov方法 比较定理 |
Stability Properties In Terms Of Two Measures for Functional Differential Systems |
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| LIU Kai-en,YANG Guo-wei.Stability Properties In Terms Of Two Measures for Functional Differential Systems[J].Journal of Qingdao University(Natural Science Edition),2008,21(1):11-17. |
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| Authors: | LIU Kai-en YANG Guo-wei |
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| Institution: | LIU Kai-en, YANG Guo-wei (1. College ot Mathematics, Qingdao University, Qingdao 266071, China;2. College of Automation Engineering, Qingdao University, Shandong, Qingdao 266071, China) |
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| Abstract: | By using the variational Lyapunov method, the stability properties in terms of two measures for functional differential systems are investigated. First, a Razumikhin comparison theorem for differential systems is given. Furthermore, a variational comparison theorem is obtained. Applying this result, in the case that the unperturbed systems are ordinary differential systems, criteria on stability in terms of two measures for functional differential systems are established. The existing results are generalized and improved. |
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| Keywords: | functional differential systems stability in terms of two measures variational Lyapunov method comparison theorem |
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