On Equivalence of Lyapunov-Razumikhin Conditions and ISS for a Class of Time-Delay Systems

For a retarded nonlinear system with a Lipschitz nonlinearity on bounded sets outside the origin, this article proposes necessary conditions for application of the Lyapunov-Razumikhin method. The presented conditions are illustrated on the classes of linear and nonlinear homogeneous systems.

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Bibliographic Details
Published in:	IEEE transactions on automatic control Vol. 69; no. 8; pp. 5666 - 5671
Main Authors:	Efimov, D., Aleksandrov, A.
Format:	Journal Article
Language:	English
Published:	New York IEEE 01-08-2024 The Institute of Electrical and Electronics Engineers, Inc. (IEEE) Institute of Electrical and Electronics Engineers
Subjects:	Asymptotic stability Automatic Control Engineering Computer Science delay systems Delays Dynamical systems Lyapunov methods Nonlinear systems Nonlinearity Stability analysis Surveys Time delay systems Vectors
Online Access:	Get full text
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Description
Summary:	For a retarded nonlinear system with a Lipschitz nonlinearity on bounded sets outside the origin, this article proposes necessary conditions for application of the Lyapunov-Razumikhin method. The presented conditions are illustrated on the classes of linear and nonlinear homogeneous systems.
ISSN:	0018-9286 1558-2523
DOI:	10.1109/TAC.2024.3382609