Boundary Feedback Stabilization of a One-dimensional Wave Equation with Velocity Recirculation and Matched Disturbance**This work was supported by the National Natural Science Foundation of China.

In this paper, we consider the stabilization problem of a one-dimensional wave equation with velocity recirculation and boundary matched general external disturbance. Active disturbance rejection control method is adopted to estimate the disturbance by distributed parameter system instead of usual high-gain lumped parameter system. With the estimation of the disturbance in hand, a state observer is constructed in the following. Then we design the controller consisting two parts: one is used to compensate the disturbance; the other is to stabilize the system without the disturbance. The resulting closed-loop system admits a unique bounded solution and the solution of the original system decays exponentially. Finally, some numerical simulations are presented to illustrate the theoretical results.