Stabilization of a class of multi-inputs nonlinear systems
type: Item
instance of: scholarly article
title: Stabilization of a class of multi-inputs nonlinear systems
zbMATH Open document ID: 0806.93046
DOI: 10.1016/0167-6911(94)90084-1
author: V. Pereyra
published in: Systems \& Control Letters
publication date: 1994-07-31T00:00:00Z
review text: The authors investigate the local stabilization of an affine system \(\dot x= f(x)+ \sum^{n-1}_{n=1} u_ i g_ i(x)\) by means of state feedback. First, they gave a sufficient and necessary condition, which is that Lie algebra, Lie \((g_ 1,\dots, g_{n-1})\), generated by \(g_ 1,\dots,g_{n-1}\), has a constant dimension, for an affine system to be feedback equivalent to the reduced system \(\dot x_ 1- f(x_ 1, x_ 2)\), \(\dot x_ 2=v\), \((x_ 1,x_ 2)\in \mathbb{R}^{n-m} \times\mathbb{R}^ m\), where \(v\) is a control vector. Next, using the above idea they provide the conditions, under which the above reduced system is stabilizable. Furthermore, they present the feedback to stabilize the above-mentioned system.
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93D20
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 612401
zbMATH Keywords: affine system
zbMATH Keywords: state feedback
reviewed by: Yu Wenhuan
MaRDI profile type: Publication
full work available at URL: 0167-6911(94)90084-1
OpenAlex ID: W2061359344
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description: scientific article; zbMATH DE number 612401