Journal Article

Boundary stabilization of hyperbolic systems related to overhead cranes

Hideki Sano

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 25, issue 3, pages 353-366
Published in print September 2008 | ISSN: 0265-0754
Published online February 2008 | e-ISSN: 1471-6887 | DOI:
Boundary stabilization of hyperbolic systems related to overhead cranes

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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

Journal Article.  0 words. 

Subjects: Mathematics

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