Active disturbance rejection control for a transport equation via a differentiatior

This paper deals with the stabilization of a transport equation subject to a boundary disturbance. Our feedback design relies on the so-called strategy called active disturbance rejection control (ADRC). The unknown disturbance is estimated by Levant's differentiator and one of the feature of this differentiator is that it allows to estimate in finite-time the disturbance. We prove the existence of solutions of the closed-loop system and the global asymptotic stability of the closed-loop system. A numerical example is given to illustrate the efficiency of our strategy.