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Stabilization with Arbitrary Convergence Rate for the Schrödinger Equation Subjected to an Input Time Delay
Journal of Systems Science and Complexity ( IF 2.6 ) Pub Date : 2020-09-09 , DOI: 10.1007/s11424-020-9294-6
Yanfang Li , Hao Chen , Yaru Xie

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.



中文翻译:

输入时滞下Schrödinger方程的任意收敛率镇定。

从系统等价的角度考虑了带有输入时滞的Schrödinger方程的镇定问题。首先,介绍了从原始系统到具有任意衰减率的指数稳定系统的线性转换,也称为“目标系统”。线性变换是通过一种具有单一核函数的Volterra型集成来构造的。结果,获得了原始系统的反馈控制律。其次,推导了从目标系统到原始闭环系统的线性变换。最后,通过建立原始闭环系统与目标闭环系统之间的等价关系,获得了闭环系统具有任意衰减率的指数稳定性。

更新日期:2020-09-10
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