The only stable normal forms of affine systems under feedback are linear
type: Item
instance of: scholarly article
title: The only stable normal forms of affine systems under feedback are linear
zbMATH Open document ID: 0641.93034
DOI: 10.1016/0167-6911(87)90103-4
published in: Systems \& Control Letters
publication date: 1987-01-01T00:00:00Z
review text: It is shown for which ranges of dimensions (m,n) smooth affine control systems \(\dot x=f(x)+\sum^{m}_{i=1}u_ ig_ i(x)\), \(x\in {\mathbb{R}}^ n\), possess structurally stable normal forms with respect to the static feedback group. Such stable forms exist only if \(m=n\) or if \(m=1\) and \(n=2\) and are, in these cases, linear.
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 22E99
Mathematics Subject Classification ID: 93B10
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93D99
zbMATH DE Number: 4045586
zbMATH Keywords: Lie group
zbMATH Keywords: structural stability
zbMATH Keywords: smooth affine control systems
zbMATH Keywords: structurally stable normal forms
zbMATH Keywords: static feedback
author: Krzysztof Tchoń
MaRDI profile type: Publication
full work available at URL: 0167-6911(87)90103-4
OpenAlex ID: W2171752260
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description: scientific article; zbMATH DE number 4045586