The active disturbance rejection control approach to output feedback stabilization of an anti-stable wave equation with corrupted boundary observation

In this paper, we are concerned with the boundary output feedback stabilization for an anti-stable wave equation where the boundary observation is corrupted by a general disturbance. We cope with the disturbance by the approach of active disturbance rejection control. In contrast with the existing results, the assumptions on the derivative of the disturbance are removed. It is necessary to assume that the disturbance is Lipschitz continuous. A state observer together with a disturbance estimator is designed by using the corrupted output. Both the well-posedness and the stability of the closed-loop system are proved. The theoretical results are validated visually by some numerical simulations.