Output feedback stabilization of an unstable wave equation with general corrupted boundary observation

We consider boundary output feedback stabilization for an unstable wave equation with boundary observation subject to a general disturbance. We adopt for the first time the active disturbance rejection control approach to stabilization for a system described by the partial differential equation with corrupted output feedback. By the approach, the disturbance is first estimated by a relatively independent estimator; it is then canceled in the feedback loop. As a result, the control law can be designed almost as that for the system without disturbance. We show that with a time varying gain properly designed, the observer driven by the disturbance estimator is convergent, and that all subsystems in the closed-loop are asymptotically stable in the energy state space. We also provide numerical simulations which demonstrate the convergence results and underline the effect of the time varying gain estimator on peaking value reduction. (C) 2014 Elsevier Ltd. All rights reserved.