Diagonalization and stability of multi-time-scale singularly perturbed linear systems
type: Item
instance of: scholarly article
title: Diagonalization and stability of multi-time-scale singularly perturbed linear systems
zbMATH Open document ID: 0557.34047
DOI: 10.1016/0096-3003(85)90003-7
author: S. G. Rajalakshmi
author: G. S. Ladde
published in: Applied Mathematics and Computation
publication date: 1985-01-01T00:00:00Z
review text: The paper deals with the system \(\dot x=A_ 0(t)x+A_{01}(t)y+A_{02}(t)z\), \(\epsilon \dot y=A_{10}(t)x+A_{11}(t)y+A_{12}(t)z\), \(\mu \dot z=A_{20}(t)x+A_{21}(t)y+A_{22}(t)z,\) where \(\epsilon\) and \(\mu\) are small parameters such that \(\lim_{\epsilon \to 0}(\mu /\epsilon)=0\). A transformation (originally proposed by Chang for one-parameter systems) is developed which results in transforming the system in a diagonal form according to the three time scales. This decomposition provides a basis for qualitative and asymptotic analysis of such singularly perturbed systems. In the paper it is used for studying the stability of the perturbed system assuming that the reduced system (with \(\epsilon =\mu =0)\) is exponentially stable.
Mathematics Subject Classification ID: 34D15
zbMATH DE Number: 3888100
zbMATH Keywords: exponentially stable system
zbMATH Keywords: small parameters
zbMATH Keywords: perturbed system
reviewed by: A. L. Dontchev
MaRDI profile type: Publication
full work available at URL: 0096-3003(85)90003-7
OpenAlex ID: W2043345297
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description: scientific article; zbMATH DE number 3888100