Stabilization of nonlinear systems in the plane
type: Item
instance of: scholarly article
title: Stabilization of nonlinear systems in the plane
zbMATH Open document ID: 0666.93103
DOI: 10.1016/0167-6911(89)90010-8
author: M. Kawski
published in: Systems \& Control Letters
publication date: 1989-01-01T00:00:00Z
review text: It is shown that every small-time locally controllable system in the plane can (locally) be asymptotically stabilized by employing Hölder continuous feedback laws, as essentially was conjectured by E. Sontag. An explicit algorithm for the construction of such feedback laws is given. Typical is the system \(\dot x=u\), \(\dot y=y-x^ 3\); which cannot be asymptotically stabilized by any \(C^ 1\)-feedback law, but is asymptotically stabilized by every feedback law \(u=-ax+by^{1/3}\) with \(b>a>1\).
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93D05
zbMATH DE Number: 4091366
zbMATH Keywords: stabilization
zbMATH Keywords: Lyapunov function
zbMATH Keywords: Hölder continuous feedback laws
MaRDI profile type: Publication
full work available at URL: 0167-6911(89)90010-8
OpenAlex ID: W1966486423
cites work: Stabilization of a class of nonlinear systems by a smooth feedback control
cites work: Stabilization with relaxed controls
cites work: Q5574850
cites work: Q3200939
cites work: Q3309568
cites work: Asymptotic stabilization of two dimensional real analytic systems
cites work: Controlled stability
cites work: Remarks on smooth feedback stabilization of nonlinear systems
cites work: Control variations with an increasing number of switchings
cites work: A Lyapunov-Like Characterization of Asymptotic Controllability
cites work: Subanalytic sets and feedback control
cites work: A General Theorem on Local Controllability
description: scientific article; zbMATH DE number 4091366