Stabilization and disturbance rejection for the beam equation

We consider a system described by the Euler-Bernoulli beam equation in a bounded domain with appropriate boundary conditions. To stabilize the system, we propose a dynamic boundary controller applied at the free end of the system. We show that with the proposed controller, the closed-loop system is asymptotically stable. Moreover, we consider the case in which the output of the controller is corrupted by disturbance.