Output Feedback Stabilization and Disturbance Rejection for a Hyperbolic PDE System With Nonlinear Boundary Condition and Disturbance

ABSTRACT This article focuses on the boundary output feedback exponential stabilization and disturbance rejection for a hyperbolic partial differential equation (PDE) system with nonlinear boundary condition and unknown control‐matched disturbance. An infinite‐dimensional disturbance estimator is designed by utilizing three boundary measurement outputs to estimate the disturbance. Subsequently, a boundary output feedback stabilizing controller is designed based on the disturbance estimate, effectively compensating for the disturbance in the feedback loop. Besides conventional operator semigroup theory and Lyapunov direct approach, novel theoretical analysis methods including the techniques of boundary reflection and iterated sequence are developed to prove rigorously the well‐posedness and exponential stability of the resulting closed‐loop system. Finally, some numerical simulations are carried out to validate the theoretical conclusions and the effectiveness of the proposed methods.