2024/06/23 by Thiago Cavalheiro, Alexandre J. Santana, Cavalheiro, Thiago Matheus +3
Computer Science · Engineering · #FOS: Mathematics #Mathematical Control Systems and Analysis #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems
paper · pdf · doi:10.48550/arxiv.2406.16237
openalex publication_date 2024/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \mathfrakh 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.