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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Vydáno v:	SIAM journal on control and optimization Ročník 48; číslo 8; s. 5564 - 5582
Hlavní autoři:	Chen, Jie, Fu, Peilin, Niculescu, Silviu-Iulian, Guan, Zhihong
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.2010
Témata:	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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Abstract	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]
AbstractList	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. 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]
Author	Fu, Peilin Guan, Zhihong Chen, Jie Niculescu, Silviu-Iulian
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SubjectTerms	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
Title	An Eigenvalue Perturbation Approach to Stability Analysis, Part I: Eigenvalue Series of Matrix Operators
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