On stability and stabilization of elastic systems by time-variant feedback

We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for stabilization and asymptotic stabilization by applying a fast oscillati...

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Bibliographic Details
Published inarXiv.org
Main Authors Caiado, M I, Sarychev, A V
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 06.07.2005
Subjects
Damping
Elastic systems
Partial differential equations
Stability
Stabilization
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Summary:We study a class of elastic systems described by a (hyperbolic) partial differential equation. Our working example is the equation of a vibrating string subject to linear disturbance. The main goal is to establish conditions for stabilization and asymptotic stabilization by applying a fast oscillating control to the string. In the first situation studied we assume that system is subject to a damping force; next we consider the system without damping. We extend the tools of high-order averaging and of chronological calculus for studying stability of this distributed parameter system.
Bibliography:content type line 50
SourceType-Working Papers-1
ObjectType-Working Paper/Pre-Print-1
ISSN:2331-8422