An initial value theorem for nonlinear singularly perturbed systems
type: Item
instance of: scholarly article
title: An initial value theorem for nonlinear singularly perturbed systems
zbMATH Open document ID: 0543.34043
DOI: 10.1016/S0167-6911(84)80041-9
published in: Systems \& Control Letters
publication date: 1984-01-01T00:00:00Z
review text: Let \((x_{\epsilon},y_{\epsilon})\) be the solution (which is assumed to exist and to be unique) of the singularly perturbed system \(\dot x=f(x,y,\epsilon)\), \(x(0)=x_ 0\), \(\epsilon\) \(\dot y=g(x,y,\epsilon)\), \(y(0)=y_ 0\). Introducing Lyapunov functions for the reduced and for the boundary systems the authors give new conditions under which \((x_{\epsilon},y_{\epsilon})\) converges to the solution \((x_ 0,y_ 0)\) of the reduced system, associated with \(\epsilon =0\), uniformly on the semi-infinite time-interval \([0,+\infty)\). A comparison with other results is presented.
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 3863639
zbMATH Keywords: singularly perturbed system
zbMATH Keywords: Lyapunov functions
author: Ali Saberi
author: Hassan K. Khalil
reviewed by: A. L. Dontchev
MaRDI profile type: Publication
cites work: Singular Perturbations on the Infinite Interval
cites work: Properties of solutions of ordinary differential equations with small parameters
cites work: Q4061303
cites work: Stabilization and regulation of nonlinear singularly perturbed systems--Composite control
cites work: Q3871201
full work available at URL: s0167-6911(84)80041-9
OpenAlex ID: W2088954130
description: scientific article; zbMATH DE number 3863639