Well-posedness and stability of boundary delay equations

IF 2.8 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2026-01-01 Epub Date: 2025-12-04 DOI:10.1016/j.sysconle.2025.106307

Yassine El Gantouh , Yang Liu

引用次数: 0

Abstract

In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the existence, uniqueness, and positivity of solutions. Furthermore, we derive spectral criteria for exponential stability. The conditions on the perturbation generalize well-known criteria for the generation of domain perturbations of positive semigroup generators. As an application, we present necessary and sufficient conditions for the exponential stability of positive hyperbolic systems with time-delayed boundary conditions.

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边界延迟方程的适定性与稳定性

本文引入了边界延迟方程的概念，建立了分析具有纯时滞边界条件的线性定常系统的统一框架。建立了解的存在性、唯一性和正性的温和充分条件。进一步，我们导出了指数稳定性的谱判据。摄动的条件推广了众所周知的正半群生成域摄动的判据。作为应用，我们给出了具有时滞边界条件的正双曲型系统指数稳定性的充分必要条件。

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

Systems & Control Letters 工程技术-运筹学与管理科学

CiteScore

4.60

自引率

3.80%

发文量

144

审稿时长

6 months

期刊介绍： Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.