Abstract
In this article, we develop some general results on the properties of the reachable sets for right invariant bilinear systems with state varying on compact Lie groups. The main results consist of a characterization of the set of states reachable in arbitrary time from the identity of the group. This, under suitable assumptions, is proved to be a Lie subgroup of the underlying Lie group. We apply these results to the analysis of the controllability of particles with spin. The results are motivated by and generalize the results in another work [D. D’Alessandro, Sys. Control Lett. 41, 213–221 (2000)], where the specific model of a spin 12 particle system in an electro-magnetic field was considered.
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