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### 常微分方程-薛定谔方程耦合系统的输出反馈镇定

1. 1. 山西农业大学基础部,太谷 030801; 2. 山西财经大学资源环境学院, 太原 030006; 3. 山西大学数学科学学院,太原 030006
• 出版日期:2018-04-25 发布日期:2021-06-25

ZHANG Xiaoying, WANG Ping, FENG Hongyinping. Output Feedback Stabilization  of a Coupled ODE-Schr\"{o}dinger   Equation System[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(4): 887-897.

### Output Feedback Stabilization  of a Coupled ODE-Schr\"{o}dinger   Equation System

ZHANG Xiaoying1 ,WANG Ping2 ,FENG Hongyinping3

1. 1. Department of Basic Courses, Shanxi Agricultural University, Taigu 030801; 2. College of Resources and Environment, Shanxi University of Finance and Economics, Taiyuan 030006; 3. School of Mathematical Sciences, Shanxi University, Taiyuan 030006
• Online:2018-04-25 Published:2021-06-25

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.
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