Uniform approximation of exponential stability for 1-D wave equation with potential

IF 2.5 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

European Journal of Control Pub Date : 2025-04-09 DOI:10.1016/j.ejcon.2025.101221

Jiankang Liu , Bao-Zhu Guo

引用次数: 0

Abstract

In this paper, we investigate uniform exponential stability approximation for a one-dimensional wave equation with potential. Given the challenges in identifying the time-domain multiplier for the exponentially stable continuous system, we opt for a frequency domain approach. Through the application of the order-reduction method, we devise a novel spatially semi-discretized finite difference scheme for the continuous system. We then establish the uniform exponential stability of the semi-discretized system using the discrete version of the frequency domain method, with the discrete proof mirroring the continuous case.

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本文研究一维带势波动方程的一致指数稳定性近似。考虑到在确定指数稳定连续系统的时域乘法器方面的挑战，我们选择了频域方法。应用降阶方法，提出了一种新的连续系统的空间半离散有限差分格式。然后，我们利用频域方法的离散版本建立了半离散系统的一致指数稳定性，离散证明反映了连续情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

European Journal of Control 工程技术-自动化与控制系统

CiteScore

5.80

自引率

5.90%

发文量

131

审稿时长

1 months

期刊介绍： The European Control Association (EUCA) has among its objectives to promote the development of the discipline. Apart from the European Control Conferences, the European Journal of Control is the Association''s main channel for the dissemination of important contributions in the field. The aim of the Journal is to publish high quality papers on the theory and practice of control and systems engineering. The scope of the Journal will be wide and cover all aspects of the discipline including methodologies, techniques and applications. Research in control and systems engineering is necessary to develop new concepts and tools which enhance our understanding and improve our ability to design and implement high performance control systems. Submitted papers should stress the practical motivations and relevance of their results. The design and implementation of a successful control system requires the use of a range of techniques: Modelling Robustness Analysis Identification Optimization Control Law Design Numerical analysis Fault Detection, and so on.