About Lyapunov functionals construction for difference equations with continuous time.
type: Item
instance of: scholarly article
title: About Lyapunov functionals construction for difference equations with continuous time.
zbMATH Open document ID: 1068.39023
author: Leonid Shaikhet
published in: Applied Mathematics Letters
publication date: 2005-03-07T00:00:00Z
review text: The author considers difference equations (in continuous time) of the form \[ x(t+h_0)=F(t,x(t),x(t-h_1),x(t-h_2),\ldots) \] with the initial condition \(x(\theta)=\phi(\theta)\) for \(\theta\in [t_0-h_0-\max_{j\geq 1}h_j,t_0]\). Under some condition on \(F\) he proves a stability criterion in terms of the existence of a Lyapunov functional. The second part of the paper is devoted to two ways to construct such a Lyapunov functional.
Mathematics Subject Classification ID: 39A11
zbMATH DE Number: 2140773
zbMATH Keywords: difference equations with continuous time
zbMATH Keywords: Lyapunov functional
zbMATH Keywords: stability
reviewed by: Christian Pötzsche
MaRDI profile type: Publication
full work available at URL: j.aml.2003.06.011
OpenAlex ID: W2028865320
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DOI: 10.1016/J.AML.2003.06.011
description: scientific article; zbMATH DE number 2140773