Output feedback stabilization of a cascade ODE-Schrödinger system subject to external unknown disturbance

In this paper, we consider the output feedback exponential stabilization problem of an ODE-Schroödinger cascade systems with the external disturbance. We propose a new extended state observer (ESO) that estimates both state and disturbance, then design a stabilizing control law by utilizing the backstepping approach. The resulting closed-loop system is shown to be exponentially stable with guaranteeing that all internal systems involved are uniformly bounded.