| Issue |
ESAIM: COCV
Volume 31, 2025
|
|
|---|---|---|
| Article Number | 91 | |
| Number of page(s) | 18 | |
| DOI | https://doi.org/10.1051/cocv/2025077 | |
| Published online | 17 November 2025 | |
Accessibility condition for discrete-time linear systems on Lie groups
1
Department of Mathematics, Universidade Estadual do Norte do Paraná, Jacarezinho, Brazil
2
Department of Mathematics, State University of Maringá, Maringá, Brazil
* Corresponding author: ajsantana@uem.br
Received:
2
July
2024
Accepted:
17
September
2025
In this paper, we characterize the accessibility condition for discrete-time linear systems on Lie groups and establish a sufficient condition for local controllability. Our approach extends the concept of the Fréchet derivative to the setting of Lie groups. We construct a subalgebra based on the infinitesimal automorphisms of the system and show that if the dimension of this subalgebra is maximal, then the system is accessible. Additionally, we examine an application concerning the existence of control sets and provide illustrative examples.
Mathematics Subject Classification: 93B03 / 93B05 / 93C05 / 22E99
Key words: Discrete system / accessibility / reachable set / Lie groups
© The authors. Published by EDP Sciences, SMAI 2025
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