The Stabilization of Multi-Dimensional Wave Equation with Boundary Control Matched Disturbance

Abstract We consider boundary stabilization for a multi-dimensional wave equation with boundary control matched disturbance that depends on both time and spatial variables. The active disturbance rejection control (ADRC) approach is adopted in investigation. An disturbance estimator is designed to estimate, in real time, the disturbance, and the disturbance is canceled in the feedback loop with its approximation. All subsystems in the closed-loop are shown to be asymptotically stable. The numerical experiments are carried out to illustrate the convergence and effect of peaking value reduction.