Homogeneous Lyapunov functions and necessary conditions for stabilization
type: Item
instance of: scholarly article
title: Homogeneous Lyapunov functions and necessary conditions for stabilization
zbMATH Open document ID: 0881.93063
DOI: 10.1007/BF01211517
author: D. Aeyels
author: Rodolphe Sepulchre
published in: MCSS. Mathematics of Control, Signals, and Systems
publication date: 1998-01-27T00:00:00Z
review text: A control system is homogeneous stabilizable with respect to a dilation if there exists a homogeneous Lyapunov function of the closed-loop system. If the control system is homogeneous then the homogeneous stabilization is guaranteed by the feedback stabilization by means of an homogeneous feedback. The paper provides necessary condition for homogeneous stabilization.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93D30
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 936203
zbMATH Keywords: continuous feedback stabilization
zbMATH Keywords: necessary conditions
zbMATH Keywords: homogeneous vector fields
zbMATH Keywords: homogeneous Lyapunov function
zbMATH Keywords: homogeneous stabilization
reviewed by: Rosa Maria Bianchini
MaRDI profile type: Publication
cites work: Stabilization with relaxed controls
cites work: A necessary condition for feedback stabilization
cites work: Linearized Control Systems and Applications to Smooth Stabilization
cites work: Q4718350
cites work: Adding an integrator for the stabilization problem
cites work: Q3976550
cites work: Q3841734
cites work: Nilpotent and High-Order Approximations of Vector Field Systems
cites work: Q4046802
cites work: Q3902876
cites work: Homogeneous Lyapunov function for homogeneous continuous vector field
cites work: Stabilizability Does Not Imply Homogeneous Stabilizability for Controllable Homogeneous Systems
cites work: A Lyapunov-Like Characterization of Asymptotic Controllability
cites work: Q3998903
cites work: The structure of the level surfaces of a Lyapunov function
full work available at URL: https://doi.org/10.1007/bf01211517
OpenAlex ID: W2083774103
description: scientific article; zbMATH DE number 936203