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IMA Journal of Mathematical Control and Information Advance Access published online on February 14, 2008
IMA Journal of Mathematical Control and Information, doi:10.1093/imamci/dnm031
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© The author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Boundary stabilization of hyperbolic systems related to overhead cranes

Hideki Sano{dagger}

Computing and Communications Center, Kagoshima University, 1-21-35 Korimoto, Kagoshima 890-0065, Japan

{dagger} Email: sano{at}cc.kagoshima-u.ac.jp

Received on December 7, 2006; Accepted on September 11, 2007

In this paper, we treat the problem of stabilizing 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. In this, the mass of the cart is assumed to be not zero. 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 by using the LaSalle's invariance principle. The stabilization problem is also discussed for the case of the system with one rigid load.

Keywords: hyperbolic system; overhead crane; C0-semigroup; asymptotic stability; LaSalle's invariance principle.


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