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This article is concerned with the asymptotic behavior of a 2D overheadcrane. Taking into account the presence of a delay in the boundary, andassuming that no displacement term appears in the system, a distributed(interior) damping feedback law is proposed in order to compensate the effectof the delay. Then, invoking the frequency domain method, the solutions of theclosed-loop system are proved to converge exponentially to a stationaryposition. This improves the recent result obtained byAl-Musallam-Ammari-Chentouf, where the rate of convergence is at most ofpolynomial type.

Further results on the asymptotic behavior of a 2D overhead crane with input delays: Exponential convergence