时变时滞系统指数稳定性分析的指数加权积分不等式

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-09-01 DOI:10.1016/j.aml.2025.109730

Nuo Cheng , Wei Wang , Hong-Bing Zeng , Xinge Liu , Xian-Ming Zhang

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引用次数: 0

摘要

研究了时变时滞系统的指数稳定性问题。利用正交多项式中某些积分比的单调性，利用二阶贝塞尔-勒让德不等式的推广，在正交多项式中引入合适的系数，得到了一个新的指数加权积分不等式。这个不等式可以直接估计具有不同极限的指数加权积分，而不需要现有文献中常用的额外保守边界。利用所提出的不等式，导出了对应于两种不同时变时滞情况的两个指数稳定性判据。基于两个研究充分的实例的仿真验证了所提方法的有效性。

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Novel exponential-weighted integral inequality for exponential stability analysis of time-varying delay systems

This paper investigates the exponential stability of systems with time-varying delays. A novel exponential-weighted integral inequality is developed from the extension of the second-order Bessel–Legendre inequality by introducing suitable coefficients into orthogonal polynomials, which leverages the monotonic property of certain integral ratios derived from orthogonal polynomials. This inequality enables the direct estimation of exponential-weighted integrals with varying limits, without requiring the additional conservative bounding commonly used in existing literature. Utilizing the proposed inequality, two exponential stability criteria are derived, corresponding to two different cases of time-varying delays. Simulations based on two well-studied examples demonstrate the effectiveness of the proposed approach.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.