A note on stabilization with saturating feedback
type: Item
instance of: scholarly article
title: A note on stabilization with saturating feedback
zbMATH Open document ID: 1016.93053
author: Thomas I. Seidman
author: Houshi Li
published in: Discrete and Continuous Dynamical Systems
publication date: 2003-03-16T00:00:00Z
review text: The authors consider a distributed parameter control system \[ \dot x= Ax+ Bu, \] where \(A\) generates a \(C_0\) contractions semigroup on a Hilbert space \({\mathcal H}\) and \(B\) is a linear bounded operator from another Hilbert space \({\mathcal U}\) to \({\mathcal H}\). The basic assumption is that \(u= -B^* x\) is an asymptotically stabilizing feedback. Then they prove that the system can be stabilized even with a saturating feedback (i.e., a feedback subject to the restriction \(\|u\|\leq 1\)). In the last section of the paper the authors point out that the continuity assumption about \(B\) can be relaxed.
reviewed by: Andrea Bacciotti
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 93C25
zbMATH DE Number: 1882980
zbMATH Keywords: stabilization
zbMATH Keywords: saturation
zbMATH Keywords: distributed parameter control system
zbMATH Keywords: saturating feedback
MaRDI profile type: Publication
full work available at URL: dcds.2001.7.319
OpenAlex ID: W1971004260
DOI: 10.3934/DCDS.2001.7.319
description: scientific article; zbMATH DE number 1882980