Attractors and partial stability of nonlinear dynamical systems.
type: Item
instance of: scholarly article
title: Attractors and partial stability of nonlinear dynamical systems.
zbMATH Open document ID: 1041.93043
author: Iliya V. Miroshnik
published in: Automatica
publication date: 2004-03-14T00:00:00Z
review text: The paper presents a study of two (very similar, but not, in general, identical) concepts: the first is a concept of attracting invariant sets (submanifolds), the other is a concept of partially asymptotic stable systems. The paper establishes relations between their local properties and enables to unify the methodologies of their analysis. By using recent results of the stability theory and techniques of the geometric theory of control, Lyapunov-like sufficient conditions of partial stability and set attractivity are proposed. Simplified solutions for the problems of set attractivity and partial stability are obtained.
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 2056277
zbMATH Keywords: nonlinear systems
zbMATH Keywords: attractors
zbMATH Keywords: partial stability
zbMATH Keywords: Lyapunov functions
zbMATH Keywords: attracting invariant sets
MaRDI profile type: Publication
full work available at URL: j.automatica.2003.10.016
OpenAlex ID: W2006999246
cites work: Controlled Lagrangians and the stabilization of mechanical systems. I: The first matching theorem.
cites work: Q4702962
cites work: Nonlinear control systems: An introduction
cites work: Q3029380
cites work: Nonlinear adaptive control of permanent magnet step motors
cites work: Q4490866
cites work: Partial stability and geometric problems of nonlinear dynamics
cites work: Q4885523
cites work: Nonlinear systems. Analysis, stability, and control
cites work: Q4371289
DOI: 10.1016/J.AUTOMATICA.2003.10.016
description: scientific article; zbMATH DE number 2056277