Multiple time scales for nonlinear systems
type: Item
instance of: scholarly article
title: Multiple time scales for nonlinear systems
zbMATH Open document ID: 0614.34058
DOI: 10.1007/BF01600193
author: R. Silva-Madriz
author: S. Shankar Sastry
published in: Circuits, Systems, and Signal Processing
publication date: 1986-01-01T00:00:00Z
review text: This paper extends the results on the multiple time-scale structure for linear autonomous systems of the form \(\dot x=A(\epsilon)x\), where A(\(\epsilon)\) is analytic in the small parameter \(\epsilon \in [0,\epsilon_ 0]\), to the nonlinear case \(\dot x=q(z,\epsilon)\), where \(q\in C^ r\), r some large integer. The main result of the work is in obtaining conditions under which the linearized system and the nonlinear system around an equilibrium point have the same time-scale structure. It is proved that analytically the time-scale structure does not follow directly from the linearized equations around the equilibrium point. However, in practice the linearized equations predict the correct time- scale structure if we restrict our system to the domain where the linearized equations approximate the nonlinear system. The paper is clearly written.
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 3994063
zbMATH Keywords: multiple time-scale structure
zbMATH Keywords: small parameter
zbMATH Keywords: equilibrium point
MaRDI profile type: Publication
cites work: Hierarchical aggregation of linear systems with multiple time scales
cites work: Input-output description of linear systems with multiple time-scales†
cites work: Geometric singular perturbation theory for ordinary differential equations
cites work: Applications of centre manifold theory
cites work: Jump behavior of circuits and systems
full work available at URL: https://doi.org/10.1007/bf01600193
OpenAlex ID: W2015330359
description: scientific article; zbMATH DE number 3994063