Stabilization of a non-linear rotating flexible structure under the presence of time-dependent delay term in a dynamic boundary control

This paper is concerned with the feedback stabilization problem for a rotating rigid body-beam system via a torque control exerted on the rigid body and a time-dependent delayed dynamic boundary force control acting at the free end of the beam. Sufficient conditions on the angular velocity of the rigid body and the delay term are derived to assure the existence and uniqueness of solutions to the system. Furthermore, the energy method approach is employed to establish the exponential stability of the closed-loop system under stronger but reasonable assumptions.