An accessibility condition for discrete-time linear systems on Lie groups
Optimization and Control
2024-06-25 v1
Abstract
In this paper, we characterize the accessibility of discrete-time linear control systems on Lie groups. Using an exceptional notion of derivative, we construct a subalgebra based on the infinitesimal automorphism of the system such that if its dimension is maximal, the system is accessible. Our criteria provide simple conditions in a general context for the discrete-time case. Additionally, we prove a sufficient condition for local controllability at the identity using the infinitesimal automorphism, akin to the ad-rank condition in the continuous case.
Cite
@article{arxiv.2406.16237,
title = {An accessibility condition for discrete-time linear systems on Lie groups},
author = {Thiago Matheus Cavalheiro and Alexandre José Santana and Eduardo Celso Viscovini},
journal= {arXiv preprint arXiv:2406.16237},
year = {2024}
}