KMS Of Academy of mathematics and systems sciences, CAS
| Order reduction-based uniform approximation of exponential stability for one-dimensional Schrodinger equation | |
| Liu, Jiankang1; Hao, Ruiqi1; Guo, Bao-Zhu2,3,4 | |
| 2022-02-01 | |
| Source Publication | SYSTEMS & CONTROL LETTERS
 |
| ISSN | 0167-6911 |
| Volume | 160Pages:9 |
| Abstract | 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. |
| Keyword | Schrodinger equation Exponential stability Uniform approximation Order reduction method |
| DOI | 10.1016/j.sysconle.2022.105136 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | National Natural Science Foundation of China[11901365] ; National Natural Science Foundation of China[61873260] ; National Natural Science Foundation of China[12131008] |
| WOS Research Area | Automation & Control Systems ; Operations Research & Management Science |
| WOS Subject | Automation & Control Systems ; Operations Research & Management Science |
| WOS ID | WOS:000788748900001 |
| Publisher | ELSEVIER |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/60385 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Liu, Jiankang |
| Affiliation | 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 |
| Recommended Citation 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. |
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