Title: Asymptotic analysis of a 2D overhead crane with input delays in the boundary control,
Abstract: The paper investigates the asymptotic behavior of a 2D overhead crane with
input 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 on
the velocity but under the presence of time-delays. We end-up with a
closed-loop system where no displacement term is involved. It is shown that the
problem is well-posed in the sense of semigroups theory. LaSalle's invariance
principle is invoked in order to establish the asymptotic convergence for the
solutions of the system to a stationary position which depends on the initial
data. Using a resolvent method it is proved that the convergence is indeed
polynomial.