Nondissipative torque and shear force controls of a rotating flexible structure

This paper is concerned with the feedback stabilization problem of a rotating disk with a flexible beam attached to its center. We propose a torque control applied on the disk and a shear force control exerted at the free end of the beam which lead to a nondissipative closed-loop system. Despite this situation, we prove that the system can be nonuniformly exponentially stabilized provided that the angular velocity of the disk is less than the square root of the first eigenvalue of the self-adjoint positive operator of the open-loop system. This result is illustrated by a set of numerical simulations.