Fractional exponential stability of nonlinear conformable fractional-order delayed systems with delayed impulses and its application

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2024-10-24 DOI:10.1016/j.jfranklin.2024.107353

Lingao Luo , Lulu Li , Jinde Cao , Mahmoud Abdel-Aty

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引用次数: 0

Abstract

This article studies the fractional exponential stability (FES) of nonlinear conformable fractional-order delayed systems (CFODSs) and the fractional exponential synchronization of conformable fractional-order delayed inertial neural networks (CFODINNs), both with delayed impulses (DIs). Under the conformable fractional-order derivative framework, a novel Halanay inequality is established by generalizing the average impulsive interval (AII), which is a key basis for further investigations. Additionally, based on the proposed inequality, the requirement of the magnitude relationship among the system delay, the impulsive intervals, and the impulsive delays is removed. Moreover, using the improved average impulsive delay (AID), a relaxed FES criterion for nonlinear CFODSs with DIs is derived. Furthermore, as an application of the obtained theoretical results, the fractional exponential synchronization of CFODINNs with DIs is studied. Finally, simulations are given to illustrate the validity of our results, where the positive effect of impulsive delays is verified.

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具有延迟脉冲的非线性保形分数阶延迟系统的分数指数稳定性及其应用

本文研究了非线性可保形分数阶延迟系统（CFODS）的分数指数稳定性（FES）和可保形分数阶延迟惯性神经网络（CFODINN）的分数指数同步性，两者都具有延迟脉冲（DI）。在可保形分数阶导数框架下，通过概括平均脉冲间隔（AII）建立了一个新的哈拉内不等式，为进一步研究奠定了重要基础。此外，基于所提出的不等式，取消了对系统延迟、脉冲间隔和脉冲延迟之间大小关系的要求。此外，利用改进的平均脉冲延迟 (AID)，还推导出了一种适用于具有 DIs 的非线性 CFODS 的宽松 FES 准则。此外，作为所获理论结果的应用，还研究了带 DI 的 CFODINN 的分数指数同步。最后，我们给出了模拟来说明我们结果的有效性，其中验证了脉冲延迟的积极作用。

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

Journal of The Franklin Institute-engineering and Applied Mathematics 工程技术-工程：电子与电气

CiteScore

7.30

自引率

14.60%

发文量

586

审稿时长

6.9 months

期刊介绍： The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.