The stabilization problem for the Schr?dinger 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 w...The stabilization problem for the Schr?dinger 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.展开更多
基金supported by the Doctoral Scientific Research Foundation of Henan Normal University under Grant No.qd18088the Natural Science Foundation of China under Grant No.61773277the Central University Basic Scientific Research Project of Civil Aviation University of China under Grant No.3122019140。
文摘The stabilization problem for the Schr?dinger 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.
