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Stabilization with Arbitrary Convergence Rate for the Schrödinger Equation Subjected to an Input Time Delay

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Abstract

The stabilization problem for the Schrödinger 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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Authors and Affiliations

  1. College of Mathematics and Information Science, Henan Normal University, Xinxiang, 453007, China

    Yanfang Li, Hao Chen & Yaru Xie

  2. School of Mechatronical Engineering, Beijing Institute of Technology, Beijing, 100081, China

    Yanfang Li, Hao Chen & Yaru Xie

  3. Department of Mathematics, Civil Aviation University of China, Tianjin, 300300, China

    Yanfang Li, Hao Chen & Yaru Xie

Authors
  1. Yanfang Li
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  2. Hao Chen
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  3. Yaru Xie
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Corresponding authors

Correspondence to Yanfang Li, Hao Chen or Yaru Xie.

Additional information

This research was supported by the Doctoral Scientific Research Foundation of Henan Normal University under Grant No. qd18088, the Natural Science Foundation of China under Grant No. 61773277 and the Central University Basic Scientific Research Project of Civil Aviation University of China under Grant No. 3122019140.

This paper was recommended for publication by Editor HU Xiaoming.

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Li, Y., Chen, H. & Xie, Y. Stabilization with Arbitrary Convergence Rate for the Schrödinger Equation Subjected to an Input Time Delay. J Syst Sci Complex 34, 975–994 (2021). https://doi.org/10.1007/s11424-020-9294-6

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  • DOI: https://doi.org/10.1007/s11424-020-9294-6

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