An Eigenvalue Perturbation Approach to Stability Analysis, Part I: Eigenvalue Series of Matrix Operators

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,...

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Veröffentlicht in:SIAM journal on control and optimization Jg. 48; H. 8; S. 5564 - 5582
Hauptverfasser: Chen, Jie, Fu, Peilin, Niculescu, Silviu-Iulian, Guan, Zhihong
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2010
Schlagworte:
Algebra
Applied sciences
Asymptotic properties
Computer science; control theory; systems
Control system analysis
Control system synthesis
Control theory. Systems
Eigenvalues
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Linear equations
Linear systems
Mathematical analysis
Mathematical models
Mathematics
Matrix
Operator theory
Operators
Perturbation methods
Sciences and techniques of general use
Stability analysis
Studies
Asymptotic behavior
Control synthesis
47A55
asymptotic analysis
eigenvalue series
Delay system
47A75
Delay
34E05
15A18
Asymptotic stability
matrix perturbation
Perturbation method
Linear time invariant system
Linear system
93D20
time-delay systems
Linear stability
Eigenvalue problem
Delay time
Asymptotic approximation
System analysis
stability
ISSN:0363-0129, 1095-7138
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Beschreibung
Zusammenfassung: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. [PUBLICATION ABSTRACT]
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ISSN:0363-0129
1095-7138
DOI:10.1137/080741707