Boundedness of orbits and stability of closed sets
type: Item
instance of: scholarly article
title: Boundedness of orbits and stability of closed sets
zbMATH Open document ID: 1187.37021
author: Sanjay P. Bhat
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2009-10-09T00:00:00Z
review text: The author establishes some new results concerning Lyapunov stability and attractivity of a closed but not necessarily compact set, and boundedness of orbits. Namely, he investigates fundamental connections between boundedness of orbits, and stability and attractivity of closed sets. For this purpose, the author makes use of topological notions of stability and attractivity which do not depend on a metric. Some examples are also given to illustrate the results obtained.
Mathematics Subject Classification ID: 37B25
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 5612962
zbMATH Keywords: stability of sets
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: attractivity
zbMATH Keywords: boundedness
zbMATH Keywords: prolongations
zbMATH Keywords: nontangency
reviewed by: Cemil Tunç
MaRDI profile type: Publication
full work available at URL: j.na.2009.04.038
OpenAlex ID: W2038271234
cites work: Q5614853
cites work: Q5440982
cites work: Separation results for the stabilization of nonlinear systems using different high-gain observer designs
cites work: Nontangency-Based Lyapunov Tests for Convergence and Stability in Systems Having a Continuum of Equilibria
cites work: Adaptive stabilization of linear systems with unknown high-frequency gains
cites work: Q5341998
cites work: Q3270074
cites work: Stability theory and the existence of periodic solutions and almost periodic solutions
cites work: A Smooth Converse Lyapunov Theorem for Robust Stability
cites work: Stability theory by Liapunov's direct method
cites work: Smoothing Derivatives of Functions and Applications
cites work: Q5630019
cites work: Q5330830
cites work: Set-valued analysis
cites work: Variational Analysis
DOI: 10.1016/J.NA.2009.04.038
description: scientific article; zbMATH DE number 5612962