考虑带有薛定谔方程执行动态的常微分方程的镇定问题. 通过在常微分方程系统上应用Backstepping方法设计出状态反馈和基于观测器的输出反馈. 与偏微分方程Backstepping方法不同, 常微分方程Backstepping方法的核函数更加简单. 文章证明了闭环系统的适定性和指数稳定性,并且给出了数值模拟来验证理论结果.

In this paper, we consider the stabilization of an ODE system through an actuator dynamics dominated by one dimensional Schr\"{o}dinger equation. By applying the backstepping transformation to the ODE system, both the full state feedback and the observer based output feedback are designed. Different from the PDE backstepping method, the kernel of the ODE backstepping is much simpler. The well-posedness and the exponential stability of the closed-loop system are proved. Some numerical simulations are given to validate the theoretical results.