### Stabilization with Arbitrary Convergence Rate for the Schr¨odinger Equation Subjected to an Input Time Delay

LI Yanfang · CHEN Hao · XIE Yaru

1. College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China; School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100081, China; Department of Mathematics,Civil Aviation University of China, Tianjin 300300, China.
Email: 2018020@htu.edu.cn; 3120185116@bit.edu.cn; yaruxie@126.com.
• Online:2021-06-25 Published:2021-03-11

LI Yanfang · CHEN Hao · XIE Yaru. Stabilization with Arbitrary Convergence Rate for the Schr¨odinger Equation Subjected to an Input Time Delay[J]. Journal of Systems Science and Complexity, 2021, 34(3): 975-994.

The stabilization problem for the Schr¨odinger equation with an input time delay is considered from the view of system equivalence. First, a linear transform from the original system into an exponentially stable system with arbitrary decay rate, also called “target system”, is introduced. The linear transform is constructed via a kind of Volterra-type integration with singular kernels functions. As a result, a feedback control law for the original system is obtained. Secondly, a linear transform from the target system into the original closed-loop system is derived. Finally, the exponential stability with arbitrary decay rate of the closed-loop system is obtained through the established equivalence between the original closed-loop system and the target one. The authors conclude this work with some numerical simulations giving support to the results obtained in this paper.

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