Exponential stabilization of a non-uniform rotating disk-beam system via a torque control and a finite memory type dynamic boundary control

This paper is consecrated to the feedback stabilization of the rotating disk-beam system. The beam is assumed to be non-uniform and clamped at its left-end to the center of the disk where a torque control takes place, while a memory boundary control is acting at the right-end of the beam. First, the usual torque control is proposed, whereas the boundary control is designed by taking into account a special type of a memory phenomenon, as well as the dynamic features of the input. Sufficient conditions on the angular velocity of the disk and the memory term are derived to guarantee the existence and uniqueness of solutions of the system. Furthermore, the frequency domain method is utilized in order to achieve the exponential stability of the closed-loop system. The relevance of the theoretical outcomes is shown through several numerical simulations.