Stability analysis of systems with time-varying delays for conservatism and complexity reduction

IF 2.1 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2024-10-23 DOI:10.1016/j.sysconle.2024.105948

Yu-Long Fan , Chuan-Ke Zhang , Yun-Fan Liu , Yong He , Qing-Guo Wang

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Abstract

This paper is concerned with the stability analysis of systems with time-varying delays via the Lyapunov–Krasovskii functional (LKF) method. Unlike the most existing works primarily on conservatism reduction, this paper aims to establish stability criteria with less conservatism as well as low complexity, based on a relatively simple LKF with improved derivative treatments. For this purpose, a fragmented-component-based integral inequality is developed through matrix-separation and mixed estimation of the augmented integral term, which tights the estimation gap and contributes to conservatism reduction; and a novel linearized transformation method is proposed by stripping-simplification and matrix-injection, which handles nonlinear delay-itself-related terms at a low complexity cost. Then, a novel stability criterion as well as several comparative criteria are obtained for linear time-delay systems. Finally, the superiority of the proposed methods is demonstrated via two benchmark examples and a load frequency control system.

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对具有时变延迟的系统进行稳定性分析，以减少保守性和复杂性

本文关注通过 Lyapunov-Krasovskii 函数（LKF）方法对具有时变延迟的系统进行稳定性分析。与大多数以降低保守性为主要目的的现有著作不同，本文旨在基于相对简单的 LKF 和改进的导数处理方法，建立保守性较小且复杂性较低的稳定性标准。为此，本文通过矩阵分离和对增强积分项的混合估计，开发了一种基于片段成分的积分不等式，它弥补了估计差距，有助于降低保守性；并通过剥离简化和矩阵注入，提出了一种新型线性化变换方法，它能以较低的复杂度成本处理非线性延迟自相关项。然后，针对线性时延系统提出了一种新的稳定性准则和几种比较准则。最后，通过两个基准实例和一个负载频率控制系统证明了所提方法的优越性。

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.