Stability of nonlinear systems with three time scales
type: Item
instance of: scholarly article
title: Stability of nonlinear systems with three time scales
zbMATH Open document ID: 0627.34063
DOI: 10.1007/BF01599620
author: B. George
published in: Circuits, Systems, and Signal Processing
publication date: 1986-01-01T00:00:00Z
review text: We study the asymptotic stability of a singularly perturbed nonlinear time-invariant system \({\mathcal S}_{\epsilon \nu}\), which has three vastly different time scales. The system \({\mathcal S}_{\epsilon \nu}\) is approximated by three simpler systems over different time intervals. We give a straightforward proof of the fact that the asymptotic stability of \({\mathcal S}_{\epsilon \nu}\) is guaranteed when the equilibrium points of the three simpler systems are exponentially stable and when the parameters \(\epsilon\) and \(\nu\) are sufficiently small.
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 4019530
zbMATH Keywords: asymptotic stability
zbMATH Keywords: singularly perturbed nonlinear time-invariant system
zbMATH Keywords: time scales
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01599620
OpenAlex ID: W2041730507
description: scientific article; zbMATH DE number 4019530