不等式的推广以及在加性时变时滞系统中的应用

数学物理学报 ›› 2024, Vol. 44 ›› Issue (5): 1335-1351.

不等式的推广以及在加性时变时滞系统中的应用

樊天娇(),冯立超^*(),杨艳梅()

华北理工大学理学院河北唐山 063210

收稿日期:2023-07-11 修回日期:2023-11-28 出版日期:2024-10-26 发布日期:2024-10-16
通讯作者: *冯立超, E-mail: fenglichao19820520@163.com
作者简介:樊天娇, E-mail: Fantianjiao@stu.ncst.edu.cn;|杨艳梅, E-mail: yanmyang@163.com
基金资助:
教育部人文社会科学研究规划基金(23YJAZH031);河北省自然科学基金(A2023209002);河北省自然科学基金(A2019209005);唐山市科学技术研究与发展计划项目(19130222g)

Generalization of Inequality and Its Application in Additive Time-Varying Delay Systems

Fan Tianjiao(),Feng Lichao^*(),Yang Yanmei()

College of Sciences, North China University of Science and Technology, Hebei Tangshan 063210

Received:2023-07-11 Revised:2023-11-28 Online:2024-10-26 Published:2024-10-16
Supported by:
Humanities and Social Science Fund of Ministry of Education(23YJAZH031);Natural Science Foundation of Hebei Province(A2023209002);Natural Science Foundation of Hebei Province(A2019209005);Tangshan Science and Technology Bureau Program of Hebei Province(19130222g)

摘要/Abstract

摘要：

该文主要研究积分不等式的改进问题, 并将其应用于加性时变时滞系统的稳定性研究: 首先, 采用含参函数构造方法, 从单调性和增加正项两个角度, 对现有的 Wirtinger 不等式进行了证明; 其次, 提出了扩展不等式, 其中包括扩展 Wirtinger 不等式和基于三阶矩阵的扩展互凸不等式; 再次, 分别利用这两个扩展不等式, 以线性矩阵不等式的形式给出了加性时变时滞系统渐近稳定的判定准则; 最后, 通过数值算例说明所提方法的优越性.

关键词: 加性时变时滞系统, Wirtinger 不等式, 稳定性分析

Abstract:

This article mainly studies the improvement problem of integral inequality and applies it to the stability study of additive time-varying delay systems: Firstly, the existing Wirtinger inequality is proven from the perspectives of monotonicity and adding positive terms using the method of constructing parameter functions. Secondly, we propose extended inequalities, including the extended Wirtinger inequality and the extended cross-convex inequality which is based on third-order matrices. Thirdly, utilizing these two extended inequalities, we provide criteria for determining the asymptotic stability of additive time-varying delay systems in the form of Linear Matrix Inequalities (LMIs). Finally, numerical examples are presented to demonstrate the effectiveness and superiority of the proposed method.

Key words: Additive time-varying delay system, Wirtinger inequality, Stability analysis

中图分类号:

O211

樊天娇, 冯立超, 杨艳梅. 不等式的推广以及在加性时变时滞系统中的应用[J]. 数学物理学报, 2024, 44(5): 1335-1351.

Fan Tianjiao, Feng Lichao, Yang Yanmei. Generalization of Inequality and Its Application in Additive Time-Varying Delay Systems[J]. Acta mathematica scientia,Series A, 2024, 44(5): 1335-1351.

图/表 6

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表6.1

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表6.4

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