| 线性常微分方程系统的稳定性 |
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| 引用本文： | 武冬.线性常微分方程系统的稳定性[J].数学年刊A辑(中文版),2003(1). |
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| 作者姓名： | 武冬 |
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| 作者单位： | 青岛海洋大学数学系 山东 |
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| 摘 要： | 本文用矩阵的Lozinskii测度的方法,得到了线性常微分方程系统的某些稳定性准则.导出了关于线性系统χ'=A(t)χ稳定性的充要条件.对于A是常数或周期矩阵的情形,我们的结果与从Jordan标准型和Floquet理论得到的经典结论相同.
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| 关 键 词： | 稳定性 线性常微分方程 矩阵的Lozinskii测度 |
STABILITY OF LINEAR ORDINARY DIFFERENTIAL SYSTEMS |
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| WU Dong.STABILITY OF LINEAR ORDINARY DIFFERENTIAL SYSTEMS[J].Chinese Annals of Mathematics,2003(1). |
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| Authors: | WU Dong |
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| Institution: | WU DongDepartment of Mathematics,Ocean Univerity of Qingdao,Qingdao 266071,Shandong,China. |
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| Abstract: | In this paper stability criteria are obtained for linear systems of ordinary differential equations by the methods involving the Lozinskii measures of matrices. For the linear system x' - A(t)x, necessary and sufficient conditions for stability are derived, and for the case that A is constant or periodic matrix, these results are equivalent to the classical results from the Jordan canonical form and the Floquet Theory. |
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| Keywords: | Liapunov stability Linear ODE Lozinskii measures of matrices |
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