Abstract
The stabilization problem of a 1D Schrödinger equation subject to boundary control is concerned in this paper. The control input is suffered from time delay. A “partial state” predictor is designed for the system and undelayed system is deduced. Based on the undelayed system, a feedback control strategy is designed to stabilize the original system. The exact observability of the dual one of the undelayed system is checked. Then it is shown that the system can be stabilized exponentially under the feedback control.
Acknowledgements
The authors thank the Editor in-Chief, the Associate Editors and the anonymous referees for their useful and helpful comments and suggestions. This work was revised while Zhong-Jie Han was a visiting member of “PDEs, Control and Numerics” team at Basque Center for Applied Mathematics (BCAM).
Notes
No potential conflict of interest was reported by the authors.