On the spectrum-determined growth condition of a vibration cable with a tip mass

Author

Guo, Baozhu ; Xu, Cheng-Zhong

Author_Institution

Dept. of Appl. Math., Beijing Inst. of Technol., China

Volume

45

Issue

1

fYear

2000

fDate

1/1/2000 12:00:00 AM

Firstpage

89

Lastpage

93

Abstract

We show that the spectrum-determined growth condition holds for the closed-loop system of a vibration cable with a tip mass and linear boundary feedback control. The optimal decay rate of the energy for a case left unsolved previously is determined, and the asymptotic expansion of the associated semigroup is obtained. As a consequence of the approach, we show, in a different point of view, the lack of uniform exponential stability of the system with only boundary velocity feedback control

Keywords

asymptotic stability; closed loop systems; feedback; asymptotic expansion; boundary velocity feedback control; closed-loop system; linear boundary feedback control; optimal decay rate; spectrum-determined growth condition; tip mass; uniform exponential stability; vibration cable; Angular velocity control; Control systems; Eigenvalues and eigenfunctions; Feedback control; Force control; Force feedback; Linear feedback control systems; Stability; Vibration control; Weight control;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.827360

Filename

827360