Lyapunov approach to boundary stabilization of an anti-stable heat equation with boundary disturbance

In this paper, we are considered with the boundary output feedback stabilization of a one-dimensional anti-stable heat equation subject to general control matched disturbance. The active disturbance rejection control (ADRC) approach is proposed in investigation. Using output of the system, we first design a variable structure state observer to the original system which is proved to be exponentially convergent. Next, the estimation of the disturbance is obtained by extended state observer for an ODEs obtained from the observer. Finally, the estimation of disturbance is used to cancel the disturbance in the output feedback controller. The stability of the resulting closed-loop system is proven.