{"title":"Weak condition for the existence of control sets with a nonempty interior for linear control systems on nilpotent groups","authors":"Adriano Da Silva, Anderson F. P. Rojas","doi":"10.1007/s00498-024-00395-4","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we show that for a linear control system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior, as soon as one impose a compactness assumption on the generalized kernel of the drift. Moreover, this control set is unique and contains the singularities of the drift in its closure.</p>","PeriodicalId":51123,"journal":{"name":"Mathematics of Control Signals and Systems","volume":"54 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of Control Signals and Systems","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s00498-024-00395-4","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we show that for a linear control system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior, as soon as one impose a compactness assumption on the generalized kernel of the drift. Moreover, this control set is unique and contains the singularities of the drift in its closure.
期刊介绍：
Mathematics of Control, Signals, and Systems (MCSS) is an international journal devoted to mathematical control and system theory, including system theoretic aspects of signal processing.
Its unique feature is its focus on mathematical system theory; it concentrates on the mathematical theory of systems with inputs and/or outputs and dynamics that are typically described by deterministic or stochastic ordinary or partial differential equations, differential algebraic equations or difference equations.
Potential topics include, but are not limited to controllability, observability, and realization theory, stability theory of nonlinear systems, system identification, mathematical aspects of switched, hybrid, networked, and stochastic systems, and system theoretic aspects of optimal control and other controller design techniques. Application oriented papers are welcome if they contain a significant theoretical contribution.
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