Dynamic stabilization of an Euler–Bernoulli beam equation with time delay in boundary observation

An Euler–Bernoulli beam equation under boundary control and delayed observation is considered. An observer–predictor based scheme is developed to stabilize the equation. On a time interval where the observation is available, the state is tracked by the observer; when the observation is not available due to the delay, the state is estimated by the predictor. The estimation is then used in proportional feedback. It is shown that the state of closed-loop system decays exponentially for smooth initial values.