Spectral properties of pseudo-resolvents under structured perturbations

被引：2
|
作者：
Curtain, Ruth F. [2 ]
Jacob, Birgit [1 ]
机构：
[1] Univ Gesamthsch Paderborn, Dept Math, D-33098 Paderborn, Germany
[2] Univ Groningen, Dept Math & Comp Sci, NL-9700 AV Groningen, Netherlands
来源：
MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS | 2009年 / 21卷 / 01期
关键词：
Pseudo-resolvent; System nodes; Operator nodes; Structured perturbations; Location of the spectrum; DIMENSIONAL LINEAR-SYSTEMS;
D O I：
10.1007/s00498-008-0035-y
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
The changes in the spectrum caused by structured perturbations of pseudo-resolvents and operators on Banach spaces are considered. In particular, if a point is in the resolvent set of an operator, necessary and sufficient conditions for it to remain in the resolvent set under structured perturbations are given. The structured perturbations of an operator are specified by an operator node that has three generating operators and a characteristic function together with an admissible feedback operator. In addition, the robustness of stability under structured perturbations is analyzed. The results are applied to boundary control systems and impedance passive systems.
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页码：21 / 50
页数：30
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