Controller design to stabilization of Schrödinger equation with boundary input disturbance. Issue 5 (3rd April 2020)

• Record Type: Journal Article
• Authors: Cui, Haoyue; Han, Zhongjie; Xu, Genqi
• Is Part Of: Applicable analysis. Volume 99:Issue 5(2020)
• Page Start: 796
• Page End: 813
• Publication Date: 2020-04-03
• Subjects: Daomin Cao; Schrödinger equation -- nonlinear boundary control -- disturbance -- observation blind point -- asymptotic stability; 93D15 -- 93D20 -- 35B40; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1514016
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, the stabilization problem of one-dimensional Schrödinger equation with boundary disturbance is concerned. The variable structure control technique is adopted to design the nonlinear feedback controller. For the Schrödinger system, the observation blind point problem is discussed and the relationship between the initial data and observation blind point is given. According to a theorem which can be regarded as an extended version of the Lions–Lax–Milgram theorem, the existence and uniqueness of the solution for the system are proved. Finally, a sufficient condition for the asymptotic stability of the system is provided. As a remark, the asymptotic stability, which can be realized by the control, is also presented.