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

doi:10.1016/j.sysconle.2022.105346

CSpace

	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
	2022-10-01
发表期刊	SYSTEMS & CONTROL LETTERS
ISSN	0167-6911
卷号	168 页码:12
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.
关键词	Coupled wave equations Uniform exponential stability Order reduction finite -difference method
DOI	10.1016/j.sysconle.2022.105346
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China ; [61873260] ; [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:000861023500001
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/60972
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.