Decomposition of linear singularly perturbed systems
type: Item
instance of: scholarly article
title: Decomposition of linear singularly perturbed systems
zbMATH Open document ID: 0629.34060
DOI: 10.1007/BF01950998
published in: Acta Mathematica Hungarica
publication date: 1987-01-01T00:00:00Z
review text: The author considers the system of differential equations \[ (*)\quad \dot x_ 1=A_{11}x_ 1+A_{12}x_ 2+f_ 1,\quad \epsilon \dot x_ 2=A_{21}x_ 1+A_{22}x_ 2+f_ 2 \] where \(x_ i\) is a vector, \(A_{ij}=A_{ij}(t,\epsilon)\) is a matrix of appropriate dimensions, \(f_ i=f_ i(t,\epsilon)\) and \(\epsilon\) is a small parameter \((i,j=1,2)\). He gives conditions for the existence of a coordinates transformation which reduces (*) to the decoupled form \[ \dot y_ 1=A_ 1(t,\epsilon)y_ 1+f(t,\epsilon),\quad \epsilon \dot y_ 2=A_ 2(t,\epsilon)y_ 2. \] Applications to stability, control and boundary value problems are discussed.
Mathematics Subject Classification ID: 34D15
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34H05
zbMATH DE Number: 4023777
zbMATH Keywords: decoupling
zbMATH Keywords: small parameter
zbMATH Keywords: control
author: V. A. Sobolev
reviewed by: Andrea Bacciotti
MaRDI profile type: Publication
cites work: Q3506242
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full work available at URL: https://doi.org/10.1007/bf01950998
OpenAlex ID: W2034883309
description: scientific article; zbMATH DE number 4023777