Output Feedback Exponential Stabilization for a One-Dimensional Wave Equation With Control Matched Nonlinear Disturbance

Abstract

In this article, we study the output feedback exponential stabilization of a one-dimensional wave equation with control matched nonlinear disturbance. The well posedness of the open-loop system, which is essentially important for the designs of observer and controller, is verified. By designing an infinite-dimensional unknown input state observer in place of the conventional extended state observer, we estimate the total disturbance in real time. Moreover, we prove the convergence of the disturbance estimator. Based on the disturbance estimator, we design a state observer by compensating the total disturbance, and an estimated state feedback controller to exponentially stabilize the original system by means of the Riesz basis approach. Some numerical simulations are presented.