Stabilization of an Euler–Bernoulli beam equation via a corrupted boundary position feedback

In this paper, we are concerned with the stabilization of an Euler–Bernoulli beam equation with a constant disturbance on the boundary observation. A dynamic boundary controller is designed by using only the displacement measurement. We obtain that the resulting closed-loop system is asymptotically stable. Meanwhile, the estimated function is shown to be convergent to the unknown disturbance as time goes to infinite.