Order reduction-based uniform approximation of exponential stability for one-dimensional Schrodinger equation

doi:10.1016/j.sysconle.2022.105136

CSpace

	Order reduction-based uniform approximation of exponential stability for one-dimensional Schrodinger equation
	Liu, Jiankang 1; Hao, Ruiqi 1; Guo, Bao-Zhu 2,3,4
	2022-02-01
发表期刊	SYSTEMS & CONTROL LETTERS
ISSN	0167-6911
卷号	160 页码:9
摘要	This paper considers the uniform exponential stability approximation of a one-dimensional Schrodinger system with boundary damping. The continuous system is known to be exponentially stable. Firstly, the order reduction method is adopted to transform the original system into an equivalent one. Two second-order semi-discretized finite difference schemes are derived for both the transformed system and the original system, which are shown to be equivalent to each other. Secondly, the Lyapunov function method is used to prove the uniform exponential stability of the semi-discretized transformed system, which is parallel to the proof of the continuous transformed system. Finally, the solution of the semi-discretized system converges weakly to the solution of the original system and the discrete energy converges to the continuous energy. (C) 2022 Elsevier B.V. All rights reserved.
关键词	Schrodinger equation Exponential stability Uniform approximation Order reduction method
DOI	10.1016/j.sysconle.2022.105136
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11901365] ; National Natural Science Foundation of China[61873260] ; National Natural Science Foundation of China[12131008]
WOS研究方向	Automation & Control Systems ; Operations Research & Management Science
WOS类目	Automation & Control Systems ; Operations Research & Management Science
WOS记录号	WOS:000788748900001
出版者	ELSEVIER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/60385
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Jiankang
作者单位	1.Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China 2.North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China 3.Acad Sin, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Liu, Jiankang,Hao, Ruiqi,Guo, Bao-Zhu. Order reduction-based uniform approximation of exponential stability for one-dimensional Schrodinger equation[J]. SYSTEMS & CONTROL LETTERS,2022,160:9.
APA	Liu, Jiankang,Hao, Ruiqi,&Guo, Bao-Zhu.(2022).Order reduction-based uniform approximation of exponential stability for one-dimensional Schrodinger equation.SYSTEMS & CONTROL LETTERS,160,9.
MLA	Liu, Jiankang,et al."Order reduction-based uniform approximation of exponential stability for one-dimensional Schrodinger equation".SYSTEMS & CONTROL LETTERS 160(2022):9.