Weak condition for the existence of control sets with a nonempty interior for linear control systems on nilpotent groups

Adriano Da Silva; Anderson F.P. Rojas

doi:10.1007/s00498-024-00395-4

Weak condition for the existence of control sets with a nonempty interior for linear control systems on nilpotent groups

Adriano Da Silva
, Anderson F.P. Rojas

Department of Mathematics

Universidade Estadual de Campinas

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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.

Original language	English
Pages (from-to)	61-79
Number of pages	19
Journal	Mathematics of Control, Signals, and Systems
Volume	37
Issue number	1
DOIs	https://doi.org/10.1007/s00498-024-00395-4
State	Published - Mar 2025

Keywords

Control sets
Linear control systems
Nilpotent Lie groups

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10.1007/s00498-024-00395-4

Cite this

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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.",

keywords = "Control sets, Linear control systems, Nilpotent Lie groups",

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PY - 2025/3

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N2 - 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.

AB - 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.

KW - Control sets

KW - Linear control systems

KW - Nilpotent Lie groups

UR - https://www.scopus.com/pages/publications/85199330111

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AN - SCOPUS:85199330111

SN - 0932-4194

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JF - Mathematics of Control, Signals, and Systems

IS - 1

ER -

Weak condition for the existence of control sets with a nonempty interior for linear control systems on nilpotent groups

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Keywords

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