{"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}
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.
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