International Journal of Control, Vol.94, No.1, 21-29, 2021
Stabilisation of a cascaded ODE-Heat system with boundary input term incorporates both enforceable control and external unknown disturbance
In this paper, we consider the output feedback stabilisation of a cascaded ODE-Heat system with Dirichlet boundary interconnection with external disturbance flowing the control end, we design an unknown input type state observer with the disturbance estimator term with the aid of the known auxiliary system, which is used to not only stabilise this cascaded system but compensate the external disturbance simultaneously. The stabilising state feedback control is designed for the observer system by the classical backstepping transformation, which is the corresponding observer-based output feedback stabilising control for the original system. As a result, the closed-loop system is proved to be exponentially stable. Finally, the numerical simulations validate the effectiveness of this method for the system with boundary disturbance.