Lyapunov-Krasovskij approach to the robust stability analysis of time-delay systems
type: Item
instance of: scholarly article
title: Lyapunov-Krasovskij approach to the robust stability analysis of time-delay systems
zbMATH Open document ID: 1014.93031
DOI: 10.1016/S0005-1098(02)00195-4
author: A. P. Zhabko
author: V. L. Kharitonov
published in: Automatica
publication date: 2003-02-13T00:00:00Z
review text: The Andronov-Witt theorem on ``constantly acting perturbations'' of ordinary differential equations (ODEs) is extended to linear ODEs with constant delays. The well-known necessary condition of `strong' asymptotic (Lyapunov-) stability in the absence of perturbations is established by means of a quadratic Krasovskij \(V\)-functional, followed by an estimate of the perturbations on its \(V'\)-boundedness. Since terms of dependent variables are allowed in the perturbations, only local robustness can be claimed without further analysis, because a small factor does not always imply that the product of dependent variables is negligible globally.
Mathematics Subject Classification ID: 93D09
Mathematics Subject Classification ID: 93C73
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 1868217
zbMATH Keywords: time-delay system
zbMATH Keywords: robust stability
zbMATH Keywords: strong asymptotic stability
zbMATH Keywords: perturbations
zbMATH Keywords: Andronov-Witt theorem
zbMATH Keywords: Krasovsky \(V\)-functional
reviewed by: Igor Gumowski
MaRDI profile type: Publication
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full work available at URL: s0005-1098(02)00195-4
OpenAlex ID: W1981140738
description: scientific article; zbMATH DE number 1868217