Uniform exponential stability of semi-discrete scheme for observer-based control of 1-D wave equation
文献类型：期刊论文
| 作者 | Ren, Han-Jing1; Guo, Bao-Zhu1,2 |
| 刊名 | SYSTEMS & CONTROL LETTERS
 |
| 出版日期 | 2022-10-01 |
| 卷号 | 168页码:12 |
| 关键词 | Coupled wave equations Uniform exponential stability Order reduction finite -difference method |
| ISSN号 | 0167-6911 |
| DOI | 10.1016/j.sysconle.2022.105346 |
| 英文摘要 | In this paper, we consider the uniformly exponential stability of a semi-discretized coupled system generated by a 1-D wave equation under a stabilizing output feedback control. Since the control and observation are non-collocated, we first design an observer to recover the state. The closed -loop system under the observer-based feedback is composed of a two coupled wave equations. First, we transform the closed-loop system into an equivalent system by order reduction method, and the transformed system is shown to be exponentially stable by constructing a suitable Lyapunov function. As a consequence, two equivalent semi-discrete finite difference schemes are developed corresponding to the transformed system and original coupled system. Parallel to the proof of the continuous counterpart, the Lyapunov function is constructed to prove the uniformly exponential stability of the semi-discrete scheme for the transformed system, which leads to the uniformly exponential stability of the semi-discrete scheme for the original coupled system. The weak convergence of the discrete solution to the continuous counterpart is also briefly presented. (C) 2022 Elsevier B.V. All rights reserved. |
| 资助项目 | National Natural Science Foundation of China ; [61873260] ; [12131008] |
| WOS研究方向 | Automation & Control Systems ; Operations Research & Management Science |
| 语种 | 英语 |
| WOS记录号 | WOS:000861023500001 |
| 出版者 | ELSEVIER |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/60971]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Guo, Bao-Zhu |
| 作者单位 | 1.North China Elect Power Univ, Sch Math & Phys, Beijing 102206, Peoples R China 2.Acad Sinica, Acad Math & Syst Sci, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Ren, Han-Jing,Guo, Bao-Zhu. Uniform exponential stability of semi-discrete scheme for observer-based control of 1-D wave equation[J]. SYSTEMS & CONTROL LETTERS,2022,168:12. |
| APA | Ren, Han-Jing,&Guo, Bao-Zhu.(2022).Uniform exponential stability of semi-discrete scheme for observer-based control of 1-D wave equation.SYSTEMS & CONTROL LETTERS,168,12. |
| MLA | Ren, Han-Jing,et al."Uniform exponential stability of semi-discrete scheme for observer-based control of 1-D wave equation".SYSTEMS & CONTROL LETTERS 168(2022):12. |
入库方式： OAI收割
来源：数学与系统科学研究院
浏览0
下载0
收藏0
其他版本
除非特别说明，本系统中所有内容都受版权保护，并保留所有权利。