Stabilization for Euler-Bernoulli Beam Equation with Boundary Moment Control and Disturbance via a New Disturbance Estimator

We address the output feedback stabilization for a Euler-Bernoulli beam equation with boundary moment control and disturbance. The stabilization of this system has been studied in Guo et al. (J Dyn Control Syst.2014;20:539-58), where the controller is based on full state feedback. In order to derive the output feedback controller, we design a new disturbance estimator to estimate the total disturbance in the sense that the estimation error signal belongs L-2(0,infinity), and it decays exponentially if the initial state is smooth. Using the estimated total disturbance, we propose a control law to stabilize the system. Using admissibility theory, we show that the closed-loop system is exponentially stable and the signals in the disturbance estimator in the closed-loop are proved to be bounded.