用沃尔连续分数展开法分析线性控制系统的稳定性

IF 1.2 4区 综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES
Hooman Fatoorehchi
{"title":"用沃尔连续分数展开法分析线性控制系统的稳定性","authors":"Hooman Fatoorehchi","doi":"10.1007/s40009-024-01398-0","DOIUrl":null,"url":null,"abstract":"<div><p>Based on a particular continued fraction expansion, the Euclidean division scheme, and the Faddeev–LeVerrier algorithm, we propose an innovative approach to stability analysis for linear time-invariant control systems. Our method offers a comprehensive analytical framework that facilitates the determination of the range of stable controller gains for closed-loop systems, whether presented in the frequency domain or the state space. Unlike the Routh–Hurwitz criterion, our technique is exempt from the ad hoc rules that govern specific cases, thus advancing analytical rigor. Moreover, in certain scenarios, our method allows for the identification of instability midstream, thereby conserving computational resources. The proposed method is conceptually lucid and readily implementable, as exemplified by three illustrative instances.</p></div>","PeriodicalId":717,"journal":{"name":"National Academy Science Letters","volume":"47 5","pages":"555 - 559"},"PeriodicalIF":1.2000,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability Analysis of Linear Control Systems by Wall’s Continued Fraction Expansion\",\"authors\":\"Hooman Fatoorehchi\",\"doi\":\"10.1007/s40009-024-01398-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Based on a particular continued fraction expansion, the Euclidean division scheme, and the Faddeev–LeVerrier algorithm, we propose an innovative approach to stability analysis for linear time-invariant control systems. Our method offers a comprehensive analytical framework that facilitates the determination of the range of stable controller gains for closed-loop systems, whether presented in the frequency domain or the state space. Unlike the Routh–Hurwitz criterion, our technique is exempt from the ad hoc rules that govern specific cases, thus advancing analytical rigor. Moreover, in certain scenarios, our method allows for the identification of instability midstream, thereby conserving computational resources. The proposed method is conceptually lucid and readily implementable, as exemplified by three illustrative instances.</p></div>\",\"PeriodicalId\":717,\"journal\":{\"name\":\"National Academy Science Letters\",\"volume\":\"47 5\",\"pages\":\"555 - 559\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"National Academy Science Letters\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40009-024-01398-0\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"National Academy Science Letters","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s40009-024-01398-0","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0

摘要

基于特定的续分展开、欧氏除法方案和 Faddeev-LeVerrier 算法,我们提出了一种线性时不变控制系统稳定性分析的创新方法。我们的方法提供了一个全面的分析框架,有助于确定闭环系统稳定控制器增益的范围,无论是频域还是状态空间。与 Routh-Hurwitz 准则不同的是,我们的技术不受特定情况下临时规则的限制,从而提高了分析的严谨性。此外,在某些情况下,我们的方法可以识别中游的不稳定性,从而节省计算资源。所提出的方法概念清晰,易于实施,三个示例即为例证。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Stability Analysis of Linear Control Systems by Wall’s Continued Fraction Expansion

Stability Analysis of Linear Control Systems by Wall’s Continued Fraction Expansion

Stability Analysis of Linear Control Systems by Wall’s Continued Fraction Expansion

Based on a particular continued fraction expansion, the Euclidean division scheme, and the Faddeev–LeVerrier algorithm, we propose an innovative approach to stability analysis for linear time-invariant control systems. Our method offers a comprehensive analytical framework that facilitates the determination of the range of stable controller gains for closed-loop systems, whether presented in the frequency domain or the state space. Unlike the Routh–Hurwitz criterion, our technique is exempt from the ad hoc rules that govern specific cases, thus advancing analytical rigor. Moreover, in certain scenarios, our method allows for the identification of instability midstream, thereby conserving computational resources. The proposed method is conceptually lucid and readily implementable, as exemplified by three illustrative instances.

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
National Academy Science Letters
National Academy Science Letters 综合性期刊-综合性期刊
CiteScore
2.20
自引率
0.00%
发文量
86
审稿时长
12 months
期刊介绍: The National Academy Science Letters is published by the National Academy of Sciences, India, since 1978. The publication of this unique journal was started with a view to give quick and wide publicity to the innovations in all fields of science
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信