Stability Analysis and Stabilization of Fractional-Order Systems With Distributed Delay

IF 3.2 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

International Journal of Robust and Nonlinear Control Pub Date : 2024-12-03 DOI:10.1002/rnc.7750

Yi-Nan Chen, Jun-Guo Lu, Zhen Zhu

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引用次数: 0

Abstract

This paper investigates the stability and stabilization problems of fractional-order systems with distributed delays (FOSDDs). Firstly, with the frequency sweeping technique and generalized Kalman-Yakubovi $\overset{ˇ}{c}$ -Popov (KYP) lemma, a novel stability condition for FOSDDs is proposed. Secondly, based on the proposed stability condition, a robust stability condition for the uncertain FOSDDs with norm-bounded uncertainties is derived. Thirdly, based on the proposed robust stability condition, a novel stabilization condition for the uncertain FOSDDs with norm-bounded uncertainties is obtained. Finally, several numerical examples are provided to show the effectiveness of the proposed results. Moreover, in the numerical examples, the comparison of the proposed results with the existing results for FOSDDs is shown to demonstrate that the obtained results are less conservative.

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具有分布延迟的分数阶系统的稳定性分析与镇定

研究了具有分布时滞的分数阶系统的稳定性和镇定问题。首先，利用扫频技术和广义Kalman-Yakubovi co $$ \overset{\check{} }{\mathrm{c}} $$ -Popov （KYP）引理，提出了一种新的FOSDDs稳定性条件。其次，基于所提出的稳定性条件，导出了具有范数有界不确定性的不确定FOSDDs的鲁棒稳定性条件。第三，基于所提出的鲁棒稳定性条件，得到了具有范数有界不确定性的不确定FOSDDs的一种新的鲁棒稳定性条件。最后，通过数值算例验证了所提结果的有效性。通过数值算例，将所提结果与已有的FOSDDs结果进行了比较，结果表明所提结果具有较小的保守性。

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

International Journal of Robust and Nonlinear Control 工程技术-工程：电子与电气

CiteScore

6.70

自引率

20.50%

发文量

505

审稿时长

2.7 months

期刊介绍： Papers that do not include an element of robust or nonlinear control and estimation theory will not be considered by the journal, and all papers will be expected to include significant novel content. The focus of the journal is on model based control design approaches rather than heuristic or rule based methods. Papers on neural networks will have to be of exceptional novelty to be considered for the journal.