Journal Article

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

Hideki Sano

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 26, issue 2, pages 231-237
Published in print June 2009 | ISSN: 0265-0754
Published online June 2009 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/dnp011
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]

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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

Journal Article.  0 words. 

Subjects: Mathematics

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