【摘 要】
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The stabilization problem for the Schr?dinger equation with an input time delay is con-sidered 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“
【机 构】
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College of Mathematics and Information Science,Henan Normal University,Xinxiang 453007,China;School
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The stabilization problem for the Schr?dinger equation with an input time delay is con-sidered 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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