New approach to asymptotic stability: Time-varying nonlinear systems
type: Item
instance of: scholarly article
title: New approach to asymptotic stability: Time-varying nonlinear systems
zbMATH Open document ID: 0876.34060
DOI: 10.1155/S016117129700046X
author: O. Diekmann
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1997-11-25T00:00:00Z
full work available at URL: https://eudml.org/doc/47736
review text: Summary: The results of the paper concern a broad family of time-varying nonlinear systems with differentiable motions. The solutions are established in form of necessary and sufficient conditions for: 1) uniform asymptotic stability of the zero state, 2) for an exact single construction of a system Lyapunov function and 3) for an accurate single determination of the (uniform) asymptotic stability domain. They permit arbitrary selection of a function \(p(\cdot)\) from a defined functional family to determine a Lyapunov function \(\text{v} (\cdot)\), \([v(\cdot)]\), by solving \(\text{v}'(\cdot)= -p(\cdot)\) (or equivalently \(v'(\cdot)= -p(\cdot) [1-v(\cdot)])\), respectively. Illustrative examples are worked out.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 93D05
Mathematics Subject Classification ID: 93D20
zbMATH DE Number: 1046344
zbMATH Keywords: time-varying nonlinear systems
zbMATH Keywords: differentiable motions
zbMATH Keywords: uniform asymptotic stability
zbMATH Keywords: Lyapunov function
MaRDI profile type: Publication
OpenAlex ID: W2033545285
description: scientific article; zbMATH DE number 1046344