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October 2006 Stabilization of a Flexible Cable with Two Rigid Loads
Hideki Sano, Masashi Otanaka
Japan J. Indust. Appl. Math. 23(3): 225-237 (October 2006).


In this paper, we study the stabilization problem of a flexible cable with two rigid loads which is described by two kinds of hyperbolic equations. From the engineering point of view, the model can be regarded as a distributed parameter overhead crane which conveys two loads simultaneously. After deriving a control law which does not increase an energy defined for the model, we prove the asymptotic stability of the closed-loop system, using the LaSalle's invariance principle. Finally, we show that the control law works effectively through a numerical simulation.


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Hideki Sano. Masashi Otanaka. "Stabilization of a Flexible Cable with Two Rigid Loads." Japan J. Indust. Appl. Math. 23 (3) 225 - 237, October 2006.


Published: October 2006
First available in Project Euclid: 11 December 2007

zbMATH: 1134.93404
MathSciNet: MR2281506

Keywords: $C_0$-semigroup , asymptotic stability , flexible cable , LaSalle's invariance principle

Rights: Copyright © 2006 The Japan Society for Industrial and Applied Mathematics

Vol.23 • No. 3 • October 2006
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