Feedback stabilization of single-input nonlinear systems
type: Item
instance of: scholarly article
title: Feedback stabilization of single-input nonlinear systems
zbMATH Open document ID: 0638.93061
DOI: 10.1016/0167-6911(88)90053-9
author: Riccardo Marino
published in: Systems \& Control Letters
publication date: 1988-01-01T00:00:00Z
review text: The feedback stabilization problem for a scalar input nonlinear system on \({\mathbb{R}}^ n,\dot x=f(x)+g(x)u\) is considered. That is, given \(f(0)=0\), when does there exist a smooth feedback function \(u=\alpha (x)\) such that the closed-loop system \(\dot x=f(x)+g(x)\alpha (x)\) has the origin as a stable equilibrium point. The author uses the idea of partial linearization [see \textit{R. Marino}, \textit{W. M. Boothby} and \textit{D. L. Elliot}, Math. Syst. Theory 18, 97-123 (1985; Zbl 0574.93028)] of the system in order to reduce the feedback stabilization problem to a lower dimensional state space. Then standard center manifold techniques are used to give sufficient conditions for the solvability of this stabilization problem.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C15
zbMATH DE Number: 4041753
zbMATH Keywords: feedback stabilization
zbMATH Keywords: scalar input nonlinear system
zbMATH Keywords: partial linearization
zbMATH Keywords: center manifold
reviewed by: H. Nijmeijer
MaRDI profile type: Publication
full work available at URL: 0167-6911(88)90053-9
OpenAlex ID: W2022012365
cites work: Stabilization of a class of nonlinear systems by a smooth feedback control
cites work: Q3309568
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cites work: On the linear equivalents of nonlinear systems
cites work: On the largest feedback linearizable subsystem
cites work: Q3745719
description: scientific article; zbMATH DE number 4041753