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The paper investigates the asymptotic behavior of a 2D overhead crane withinput delays in the boundary control. A linear boundary control is proposed.The main feature of such a control lies in the facts that it solely depends onthe velocity but under the presence of time-delays. We end-up with aclosed-loop system where no displacement term is involved. It is shown that theproblem is well-posed in the sense of semigroups theory. LaSalle's invarianceprinciple is invoked in order to establish the asymptotic convergence for thesolutions of the system to a stationary position which depends on the initialdata. Using a resolvent method it is proved that the convergence is indeedpolynomial.

Asymptotic analysis of a 2D overhead crane with input delays in the boundary control