Converse Lyapunov theorem for Input-to-State Stability of Linear Integral Difference Equations

IF 5.9 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2025-06-17 DOI:10.1016/j.automatica.2025.112437

Maxence Lamarque , Jean Auriol , Delphine Bresch-Pietri

引用次数: 0

Abstract

This paper investigates necessary and sufficient Lyapunov conditions for Input-to-State Stability (ISS) of Linear Integral Difference Equations in the presence of an additional exogenous signal. Building on recent research in the literature pertaining to necessary conditions for the exponential stability of difference equations, we introduce a quadratic Lyapunov functional that incorporates the derivative of the so-called Lyapunov matrix. We demonstrate that the ISS of the considered class of systems is contingent upon the existence of an ISS Lyapunov functional. The Lyapunov analysis hinges on the properties of the fundamental matrix and the delay Lyapunov matrix.

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线性积分差分方程输入-状态稳定性的逆Lyapunov定理

本文研究了存在附加外源信号时线性积分差分方程输入状态稳定性的充分必要李雅普诺夫条件。基于最近关于差分方程指数稳定性的必要条件的文献研究，我们引入了一个二次Lyapunov泛函，它包含了所谓的Lyapunov矩阵的导数。我们证明了所考虑的一类系统的ISS取决于ISS Lyapunov泛函的存在。李雅普诺夫分析依赖于基本矩阵和延迟李雅普诺夫矩阵的性质。

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

Automatica 工程技术-工程：电子与电气

CiteScore

10.70

自引率

7.80%

发文量

617

审稿时长

5 months

期刊介绍： Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.