Stabilization and Riesz basis property for an overhead crane model with feedback in velocity and rotating velocity

This paper studies a variant of an overhead crane modelʹs problem, with a control force in velocity and rotating velocity on the platform. We obtain under certain conditions the well-posedness and the strong stabilization of the closed-loop system. We then analyze the spectrum of the system. Using a method due to Shkalikov, we prove the existence of a sequence of generalized eigenvectors of the system, which forms a Riesz basis for the state energy Hilbert space.