A new trajectory reversing method for estimating stability regions of autonomous nonlinear systems
type: Item
instance of: scholarly article
title: A new trajectory reversing method for estimating stability regions of autonomous nonlinear systems
zbMATH Open document ID: 0970.34047
DOI: 10.1023/A:1008311427709
author: M. Loccufier
author: E. Noldus
published in: Nonlinear Dynamics
publication date: 2001-10-13T00:00:00Z
review text: It is considered an autonomous system \(\dot{x}=f(x)\), with \(x\in \mathbb{R}^{n}, f\in C^{1}\) under the following assumptions: 1. All equilibrium points are hyperbolic. 2. There exists a global Lyapunov function \(V(x)\) such that along any nontrivial solution \(x(t)\) there does not exist a time interval \([t_{1},t_{2}]; t_{1}< t_{2}\) such that \(\dot{V}(x(t))=0\) for \(t\in [t_{1},t_{2}].\) 3. All solutions on the stability boundary remain bounded for \(t>0.\) The method uses a combination of Lyapunov theory, simulation and some properties of the geometric structure of the stability boundary.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 37B25
zbMATH DE Number: 1487127
zbMATH Keywords: autonomous system
zbMATH Keywords: stability regions
zbMATH Keywords: trajectory reversion
zbMATH Keywords: Lyapunov theory
MaRDI profile type: Publication
full work available at URL: a:1008311427709
OpenAlex ID: W147207315
Recommended article: A new trajectory reversing method for the estimation of asymptotic stability regions
Recommended article: On the estimation of asymptotic stability regions for autonomous nonlinear systems
Recommended article: Q3032631
Recommended article: A trajectory-based approach for the stability robustness of nonlinear systems with inputs
Recommended article: Exact asymptotic stability analysis and region-of-attraction estimation for nonlinear systems
Recommended article: Stability Regions of Nonlinear Dynamical Systems
Recommended article: Stability regions of nonlinear dynamical systems: a constructive methodology
Recommended article: Q5703721
Recommended article: A constructive methodology for estimating the stability regions of interconnected nonlinear systems
Recommended article: Q4036663
description: scientific article; zbMATH DE number 1487127