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IMA Journal of Mathematical Control and Information 2009 26(2):231-237; doi:10.1093/imamci/dnp011
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© The author 2009. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Supplement to: ‘Boundary stabilization of hyperbolic systems related to overhead cranes’ [H. Sano, IMA J. Math. Control Inf. (2008) vol. 25, 353–366, doi:10.1093/imamci/dnm031]

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 June 23, 2008; Revision received June 23, 2008. Accepted on April 24, 2009

In the paper cited in the heading, we treated the problem of stabilizing a flexible cable with two rigid loads, which was described by two kinds of hyperbolic equations. To show the asymptotic stability of the closed-loop system with a controller derived there, we used the LaSalle's invariance principle. However, in that paper, we need to supplement the proof of Theorem 5.1 and to revise the proof of Theorem 5.2. Throughout this note, we use the same notation as in the paper cited in the heading.

Keywords: hyperbolic system; fundamental solution; LaSalle's invariance principle.


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