Low-gain adaptive stabilization of infinite-dimensional second-order systems
type: Item
instance of: scholarly article
title: Low-gain adaptive stabilization of infinite-dimensional second-order systems
zbMATH Open document ID: 1030.93023
DOI: 10.1016/S0022-247X(02)00433-X
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The paper is devoted to the study of the low-gain adaptive stabilization of infinite-dimensional undamped second-order systems with unbounded input and output operators which are asymptotically stabilized by some scalar output feedback. The adaptive stabilizer is constructed by a low-gain adaptive PI controller (proportional plus integral controller). An energy-like (Lyapunov-like) function and a multiplier function are introduced. It is shown that the existence of these functions satisfying suitable hypotheses is fundamental to stabilize second-order systems. The author gives an example related to a linear undamped elastic string system.
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 34H05
zbMATH DE Number: 1866720
zbMATH Keywords: low-gain adaptive stabilization
zbMATH Keywords: infinite-dimensional undamped second order systems
zbMATH Keywords: PI controller
zbMATH Keywords: elastic string system
author: Toshihiro Kobayashi
reviewed by: Antonio Cañada
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00433-x
OpenAlex ID: W2040986267
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description: scientific article; zbMATH DE number 1866720