Compensation of the interior delay effect for a rotating disk-beam system

This article is dedicated to the investigation of the stabilization problem of a rotating disk-beam system. The feedback law consists of a torque control applied on the disk and a boundary force control exerted on the flexible beam, whereas a delay occurs in the interior control. Then, it is shown that the effect of the interior delay can be compensated by the action of the boundary force control. To be more precise, the closed-loop system is shown to have the very desirable property, namely the exponential stability provided that the delay term is sufficiently small and the angular velocity of the disk does not exceed an upper bound. The proof of this result depends in an essential way on the utilization of multipliers as the basis of the derivation of energy estimates.