四元数值分数阶离散记忆神经网络的耗散和耗散性分析

IF 1 4区数学 Q1 MATHEMATICS

Mathematical Control and Related Fields Pub Date : 2023-01-01 DOI:10.3934/mcrf.2023039

Hongzhi Wei, Ruoxia Li, Ning Li

{"title":"四元数值分数阶离散记忆神经网络的耗散和耗散性分析","authors":"Hongzhi Wei, Ruoxia Li, Ning Li","doi":"10.3934/mcrf.2023039","DOIUrl":null,"url":null,"abstract":"This paper illustrates the dissipative and dissipativity analysis for the fractional-order memristive system with quaternion terms. The purpose is to derive some conditions that are capable of guaranteeing the stability and dissipativity of the system. By resorting to a novel functional, sufficient conditions for the solvability of the above problem are established in the form of algebraic inequality and linear matrix inequality (LMI). In addition, based on the linear fractional difference system, the dissipativity conclusion is obtained, in which, the globally attractive sets is figured out as well. Finally, three examples are given to show the application of our proposed methods.","PeriodicalId":48889,"journal":{"name":"Mathematical Control and Related Fields","volume":"24 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dissipative and dissipativity analysis for quaternion-valued fractional-order discrete-time memristive neural networks\",\"authors\":\"Hongzhi Wei, Ruoxia Li, Ning Li\",\"doi\":\"10.3934/mcrf.2023039\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper illustrates the dissipative and dissipativity analysis for the fractional-order memristive system with quaternion terms. The purpose is to derive some conditions that are capable of guaranteeing the stability and dissipativity of the system. By resorting to a novel functional, sufficient conditions for the solvability of the above problem are established in the form of algebraic inequality and linear matrix inequality (LMI). In addition, based on the linear fractional difference system, the dissipativity conclusion is obtained, in which, the globally attractive sets is figured out as well. Finally, three examples are given to show the application of our proposed methods.\",\"PeriodicalId\":48889,\"journal\":{\"name\":\"Mathematical Control and Related Fields\",\"volume\":\"24 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Control and Related Fields\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/mcrf.2023039\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Control and Related Fields","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/mcrf.2023039","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

本文给出了具有四元数项的分数阶记忆系统的耗散和耗散分析。目的是推导出能够保证系统稳定性和耗散性的一些条件。利用一种新的泛函形式，以代数不等式和线性矩阵不等式(LMI)的形式建立了上述问题的可解性的充分条件。此外，在线性分数阶差分系统的基础上，得到了系统的耗散性结论，并给出了系统的全局吸引集。最后，给出了三个实例来说明本文方法的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Dissipative and dissipativity analysis for quaternion-valued fractional-order discrete-time memristive neural networks

This paper illustrates the dissipative and dissipativity analysis for the fractional-order memristive system with quaternion terms. The purpose is to derive some conditions that are capable of guaranteeing the stability and dissipativity of the system. By resorting to a novel functional, sufficient conditions for the solvability of the above problem are established in the form of algebraic inequality and linear matrix inequality (LMI). In addition, based on the linear fractional difference system, the dissipativity conclusion is obtained, in which, the globally attractive sets is figured out as well. Finally, three examples are given to show the application of our proposed methods.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Mathematical Control and Related Fields MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

8.30%

发文量

期刊介绍： MCRF aims to publish original research as well as expository papers on mathematical control theory and related fields. The goal is to provide a complete and reliable source of mathematical methods and results in this field. The journal will also accept papers from some related fields such as differential equations, functional analysis, probability theory and stochastic analysis, inverse problems, optimization, numerical computation, mathematical finance, information theory, game theory, system theory, etc., provided that they have some intrinsic connections with control theory.