Output Feedback Stabilization of an ODE-Schrödinger Cascade System Subject to Boundary Control Matched Unknown Disturbance

Abstract

In this paper, we consider the output feedback exponential stabilization problem of ODE-Schrodinger cascade systems with the external disturbance. We propose a new extended state observer (ESO) that estimates both state and disturbance by the three output signals, then design a stabilizing control law by utilizing the backstepping technique. The resulting closed-loop system is shown to be exponentially stable guaranteeing that all internal systems involved are uniformly bounded. Finally, some numerical experiments are carried out to verify the effectiveness of the proposed control law.