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

2005/07/06 by M. I. Caiado, Caiado, M. I., A. V. Sarychev +1
Mathematics · #34C29 #34D20 #34E05 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:34C29 #msc:34D20 #msc:34E05

paper · pdf · doi:10.48550/arxiv.math/0507123

17 pages

arxiv created 2005/07/06 · arxiv updated 2009/12/01

Abstract

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.

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