{"title":"Linear Dynamical Systems over Finite Rings","authors":"Yannic Rohde , Eva Zerz","doi":"10.1016/j.ifacol.2024.10.198","DOIUrl":null,"url":null,"abstract":"<div><div>We present the theory of linear systems over various kinds of finite commutative rings. Since these systems are finite, the trajectories have to run into repeating cycles eventually. This periodic behavior is the main interest of this topic. Using an approach similar to Fitting's lemma, a bijective-nilpotent decomposition of the system can be achieved, which in some cases even gives a decomposition of the system matrix. In particular, this allows us, to apply results about invertible system matrices, where all trajectories are purely periodic, to the more general setting. Finally, the algorithmic potential of the theory is discussed.</div></div>","PeriodicalId":37894,"journal":{"name":"IFAC-PapersOnLine","volume":"58 17","pages":"Pages 374-379"},"PeriodicalIF":0.0000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"IFAC-PapersOnLine","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2405896324019530","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
We present the theory of linear systems over various kinds of finite commutative rings. Since these systems are finite, the trajectories have to run into repeating cycles eventually. This periodic behavior is the main interest of this topic. Using an approach similar to Fitting's lemma, a bijective-nilpotent decomposition of the system can be achieved, which in some cases even gives a decomposition of the system matrix. In particular, this allows us, to apply results about invertible system matrices, where all trajectories are purely periodic, to the more general setting. Finally, the algorithmic potential of the theory is discussed.
期刊介绍：
All papers from IFAC meetings are published, in partnership with Elsevier, the IFAC Publisher, in theIFAC-PapersOnLine proceedings series hosted at the ScienceDirect web service. This series includes papers previously published in the IFAC website.The main features of the IFAC-PapersOnLine series are: -Online archive including papers from IFAC Symposia, Congresses, Conferences, and most Workshops. -All papers accepted at the meeting are published in PDF format - searchable and citable. -All papers published on the web site can be cited using the IFAC PapersOnLine ISSN and the individual paper DOI (Digital Object Identifier). The site is Open Access in nature - no charge is made to individuals for reading or downloading. Copyright of all papers belongs to IFAC and must be referenced if derivative journal papers are produced from the conference papers. All papers published in IFAC-PapersOnLine have undergone a peer review selection process according to the IFAC rules.
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