An Eigenvalue Perturbation Approach to Stability Analysis, Part I: Eigenvalue Series of Matrix Operators
An Eigenvalue Perturbation Approach to Stability Analysis, Part I: Eigenvalue Series of Matrix Operators
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DOI：
10.1137/080741707
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发表时间：
2010-09
期刊：
影响因子：
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通讯作者：
Jie Chen;Peilin Fu;S. Niculescu;Zhiho Guan
中科院分区：
文献类型：
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作者：
Jie Chen;Peilin Fu;S. Niculescu;Zhiho Guan
这两部分的文件是关于线性系统的稳定性分析参数变化，其中线性定常时滞系统是特别感兴趣的。我们试图描述这样的系统的特征零点的渐近行为。例如，这种行为决定了虚零点是否从一个半平面进入另一个半平面，因此在确定系统的稳定性方面起着关键作用。在本文的第一部分中，我们开发了必要的数学工具，这项研究的重点是全纯矩阵算子的特征值系列。而独立的兴趣，特征值摄动分析有一个特殊的关系，稳定性分析，事实上，有希望提供有效的计算解决方案的一类问题的控制系统的分析和设计，其中时滞系统是一个显着的例子。
This two-part paper is concerned with stability analysis of linear systems subject to parameter variations, of which linear time-invariant delay systems are of particular interest. We seek to characterize the asymptotic behavior of the characteristic zeros of such systems. This behavior determines, for example, whether the imaginary zeros cross from one half plane into another, and hence plays a critical role in determining the stability of a system. In Part I of the paper we develop necessary mathematical tools for this study, which focuses on the eigenvalue series of holomorphic matrix operators. While of independent interest, the eigenvalue perturbation analysis has a particular bearing on stability analysis and, indeed, has the promise to provide efficient computational solutions to a class of problems relevant to control systems analysis and design, of which time-delay systems are a notable example.