Output Feedback Stabilization for an Unstable Cascaded ODE-Heat Systems Subject to External Disturbance

In this paper, we are concerned with the output feedback exponential stabilization of cascaded parabolic PDE-ODE system where the control end suffers from the external uncertain disturbance, we design an unknown input type state observer with the disturbance estimator term, which is used to stabilize this cascaded system and compensate the external disturbance simultaneously. The stabilizing state feedback control is designed for the observer system by the three steps backstepping transformations, which is the corresponding observer based output feedback stabilizing control for the original system. Finally, the closed-loop system is shown to be exponentially stable.