Stability with mixed H ∞/passivity performance analysis of fractional-order neutral delayed Markovian jumping neural networks

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-10-17 DOI:10.1515/ijnsns-2021-0447

Narasimman Padmaja, P. Balasubramaniam

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引用次数: 1

Abstract

Abstract A detailed survey of existing works on fractional-order nonlinear systems reveals the fact that practically no results exist on stability or any performance analysis of Markovian jumping fractional-order systems (FOSs) in general. The main reason is the theory of infinitesimal generator used to estimate the derivative of Lyapunov–Krasovskii Functional (LKF) is not well-developed in the fractional domain. This shortage, in theory, is focussed in this manuscript. In this work, we provide a lemma that aids in analyzing the stability of fractional-order delayed systems via integer-order derivative of LKF. Using this lemma, by constructing a new suitable LKF and employing known integral inequalities, linear matrix inequality (LMI)-based sufficient conditions that ensure stability along with H ∞/passive performance of the proposed fractional-order neural networks (FONNs) with Markovian jumping parameters are derived for the first time. Unlike the existing works, the results derived in the present study depend on the fractional order (FO) of the NNs. The importance of such order-dependent criteria is highlighted in numerical examples. Finally, the simulation results are given to show the reliability of the derived conditions.

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分数阶中立型延迟马尔可夫跳变神经网络的混合H∞稳定性/无源性能分析

摘要对分数阶非线性系统已有的研究成果进行了详细的回顾，发现对于一般的马尔可夫跳变分数阶系统(FOSs)的稳定性和性能分析几乎没有任何结果。其主要原因是用于估计Lyapunov-Krasovskii泛函(LKF)导数的无穷小发生器理论在分数阶域上发展不够完善。从理论上讲，这一不足集中在本手稿中。在这项工作中，我们提供了一个引理，有助于通过LKF的整阶导数来分析分数阶延迟系统的稳定性。利用这一引理，通过构造一个新的合适的LKF和利用已知的积分不等式，首次导出了基于线性矩阵不等式(LMI)的具有马尔可夫跳变参数的分数阶神经网络(FONNs)具有H∞/被动稳定性的充分条件。与已有的研究不同，本研究的结果依赖于神经网络的分数阶(FO)。数值例子强调了这种顺序相关准则的重要性。最后给出了仿真结果，验证了所推导条件的可靠性。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.