Uniform exponential stability of semi-discrete scheme for observer-based control of 1-D wave equation

doi:10.1016/j.sysconle.2022.105346

	Uniform exponential stability of semi-discrete scheme for observer-based control of 1-D wave equation
	Ren, Han-Jing 1; Guo, Bao-Zhu 1,2
刊名	SYSTEMS & CONTROL LETTERS
	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
出版者	ELSEVIER
WOS记录号	WOS:000861023500001
内容类型	期刊论文
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.