Spectrum of monodromy operator for a time-delay system with application to stability analysis
Spectrum of monodromy operator for a time-delay system with application to stability analysis
复制标题
时滞系统单性算子谱及其在稳定性分析中的应用
DOI：
10.1109/tac.2015.2422479
复制
发表时间：
2015
影响因子：
6.8
通讯作者：
Tomomichi Hagiwara
中科院分区：
文献类型：
--
作者：
Jung Hoon Kim;Tomomichi Hagiwara
本文研究了在线性定常时滞反馈系统稳定性分析中起重要作用的单值算子的谱性质。注意的动机是这样一个事实，即这个操作实际上可以自然地定义在四个空间，其中的差异源于不同的选择的功能空间上的无限维状态的这样一个时间延迟系统被假定为采取其值。首先证明了单值算子的谱与其所定义的空间无关。这意味着时滞系统的稳定性与底层函数空间无关。进一步证明了算子谱在单值算子处是连续的，从而证明了单值算子的谱计算可以通过任意易处理算子的逼近来实现。数值研究相关的理论发展和建议，我们的理论研究的实际意义。
This note studies the spectral properties of monodromy operators, which play an important role in stability analysis of linear time-invariant time-delay feedback systems. The note is motivated by the fact that this operator can actually be defined naturally on four spaces, where the difference stems from different choices for the function space on which the infinite-dimensional state of such a time-delay system is assumed to take its value. It is first shown that the spectrum of the monodromy operator is independent of the spaces on which it is defined. This implies that stability of time-delay systems is independent of the underlying function spaces. It is further shown that the operator spectrum is continuous at monodromy operators, which justifies the spectrum computation of the monodromy operator through its approximation by any sort of tractable operators. A numerical study relevant to the theoretical development is provided and a practical implication of our theoretical study is suggested.