Pseudospectra and stability radii of analytic matrix functions with application to time-delay systems

W Michiels; K Green; T Wagenknecht; Silviu-Iulian Niculescu

Pseudospectra and stability radii of analytic matrix functions with application to time-delay systems

W Michiels, K Green, T Wagenknecht, Silviu-Iulian Niculescu

Department of Engineering Mathematics

Research output: Working paper

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Abstract

Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated.

Original language	English
Publication status	Published - Mar 2005

Bibliographical note

Additional information: Preprint submitted to Elsevier Science

Sponsorship: This paper presents research results of the Belgian Programme on Interuniversity
Attraction Poles, initiated by the Belgian Federal Science Policy Office. The scientifc responsibility rests with its authors. Wim Michiels is a Postdoctoral Fellow of the Fund for Scientific Research, Flanders (Belgium). Kirk Green and Thomas Wagenknecht are supported by the EPSRC grant
GR/535684/01.

Keywords

stability
pseudospectrum
robustness
delay equations

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http://hdl.handle.net/1983/925

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abstract = "Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated.",

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AU - Niculescu, Silviu-Iulian

N1 - Additional information: Preprint submitted to Elsevier Science Sponsorship: This paper presents research results of the Belgian Programme on Interuniversity Attraction Poles, initiated by the Belgian Federal Science Policy Office. The scientifc responsibility rests with its authors. Wim Michiels is a Postdoctoral Fellow of the Fund for Scientific Research, Flanders (Belgium). Kirk Green and Thomas Wagenknecht are supported by the EPSRC grant GR/535684/01.

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N2 - Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated.

AB - Definitions for pseudospectra and stability radii of an analytic matrix function are given, where the structure of the function is exploited. Various perturbation measures are considered and computationally tractable formulae are derived. The results are applied to a class of retarded delay differential equations. Special properties of the pseudospectra of such equations are determined and illustrated.

KW - stability

KW - pseudospectrum

KW - robustness

KW - delay equations

M3 - Working paper

BT - Pseudospectra and stability radii of analytic matrix functions with application to time-delay systems

ER -

Pseudospectra and stability radii of analytic matrix functions with application to time-delay systems

Abstract

Bibliographical note

Keywords

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