Existence of piecewise affine Lyapunov functions in two dimensions
type: Item
instance of: scholarly article
title: Existence of piecewise affine Lyapunov functions in two dimensions
zbMATH Open document ID: 1205.34064
author: Peter Giesl
author: Sigurdur Hafstein
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-08-11T00:00:00Z
review text: The authors consider the problem of existence of piecewise affine Lyapunov functions for autonomous systems of the form \[ \dot x=f(x) \] under the assumptions that \(f\in{C}^{1}\left(\mathbb{R}^{n},\mathbb{R}^{n}\right)\) and that the origin is an exponentially stable equilibrium of the system. The main result of the paper is a theorem which states, that in the case \(n=2\), there is a local triangulation scheme such that the system possesses a piecewise affine Lyapunov function in a neighborhood of the equilibrium.
reviewed by: Mihail Megan
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 5768944
zbMATH Keywords: piecewise affine Lyapunov functions
zbMATH Keywords: exponentially stable equilibrium
zbMATH Keywords: triangulation scheme
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.05.009
OpenAlex ID: W2138457988
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DOI: 10.1016/J.JMAA.2010.05.009
description: scientific article; zbMATH DE number 5768944