Stabilization of the cascaded ODE-Schrodinger equations subject to observation with time delay

This paper focuses on the stabilization of the cascaded Schrodinger-ODE equations subject to the observation with time delay. Both observer and predictor systems are designed to estimate the state variable on the time interval (t-tau) when the observation is available, and to predict the state variable on the time interval (t-tau) when the observation is not available, respectively. Based on the estimated state variable and the output feedback stabilizing controller using the backstepping method, it is shown that the closed-loop system is exponentially stable.