In this paper, we are concerned with the boundary output feedback stabilization problem of a Schrödinger equation with a nonlocal term. Firstly, we design an explicit boundary state feedback controller by backstepping approach. Under this controller, the closed-loop system is proved to be exponentially stable from the equivalence between the original system and the target system. Then, we propose an observer-based output feedback controller by replacing the state in state feedback controller with its estimation. The resulting closed-loop system admits a unique solution which is exponentially stable. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed feedback controller.

在本文中，我们关注具有非局部项的Schrödinger方程的边界输出反馈镇定问题。首先，我们通过反推法设计了一种显式的边界状态反馈控制器。在该控制器下，从原始系统和目标系统之间的等效性证明了闭环系统是指数稳定的。然后，通过将状态反馈控制器中的状态替换为其估计值，我们提出了一种基于观察者的输出反馈控制器。最终的闭环系统采用了独特的指数稳定解决方案。最后，给出一些数值示例来说明所提出的反馈控制器的有效性。