An accessibility condition for discrete-time linear systems on Lie groups

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 h 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.