Stabilization for Schrödinger equation with a time delay in the boundary input. Issue 5 (3rd May 2016)

• Record Type: Journal Article
• Authors: Cui, Hao-Yue; Han, Zhong-Jie; Xu, Gen-Qi
• Is Part Of: Applicable analysis. Volume 95:Issue 5(2016)
• Page Start: 963
• Page End: 977
• Publication Date: 2016-05-03
• Subjects: Schrödinger equation -- time delay -- predictor -- feedback control -- exponential stability; 35J10 -- 93C20 -- 93D15 -- 93D20; Mathematical analysis -- Periodicals; 515
• DOI: Http://www.tandfonline.com/doi/10.1080/00036811.2015.1047830
• Languages: English
• ISSNs: 0003-6811

Abstract

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.