Conditions for scale-based decompositions in singularly perturbed systems
type: Item
instance of: scholarly article
title: Conditions for scale-based decompositions in singularly perturbed systems
zbMATH Open document ID: 0641.93017
DOI: 10.1016/0024-3795(88)90173-5
author: George C. Verghese
author: Alan S. Willsky
author: Pamela G. Coxson
author: Sheldon X. C. Lou
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: From the authors abstract: ``... consider the linear systems of the form \(\dot x=A(\epsilon)x\), with A(\(\epsilon)\) analytic at 0, nonsingular for \(\epsilon \in (0,\epsilon_ 0]\), and singular at \(\epsilon =0..\). Using ideas from an algebraic approach that we have developed for the study of singularly perturbed systems, we show (among other results): that the Smith decomposition of \(A(\epsilon)\) permits transformation to a form in which the scales become explicit and the computations become transparent and simple...''
Mathematics Subject Classification ID: 93B25
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 15A21
Mathematics Subject Classification ID: 93B17
zbMATH DE Number: 4045569
zbMATH Keywords: linear systems
zbMATH Keywords: singularly perturbed systems
zbMATH Keywords: Smith decomposition
zbMATH Keywords: scales
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90173-5
OpenAlex ID: W2093584043
cites work: Q3791007
cites work: Singular perturbations and time-scale methods in control theory: Survey 1976-1983
cites work: A singular perturbation analysis of high-gain feedback systems
cites work: The McMillan and Newton polygons of a feedback system and the construction of root loci†
cites work: Asymptotic unbounded root loci--Formulas and computation
cites work: Time-scale modeling of dynamic networks with applications to power systems. Contributors: Bozidar Avramovic, Petar V. Kokotovic, George M. Peponides, James R. Winkelman
cites work: Hierarchical aggregation of singularly perturbed finite state markov processes
cites work: The reduction of perturbed Markov generators
cites work: Q3955947
cites work: Block diagonally dominant matrices and generalizations of the Gerschgorin circle theorem
cites work: Hierarchical aggregation of linear systems with multiple time scales
cites work: Algebraic approach to time scale analysis of singularly perturbed linear systems
cites work: Q3802944
cites work: Rational matrix structure
cites work: Q3902963
cites work: Q4183410
cites work: Direct singular perturbation analysis of high-gain and cheap control problems
cites work: Analytic perturbation theory for matrices and operators. Licensed ed
description: scientific article; zbMATH DE number 4045569