Linear Control Systems on Homogeneous Spaces of the Heisenberg Group

Let H denote the 3-dimensional Heisenberg Lie group. The main purpose of this paper is to classify all possible linear control systems on the homogeneous spaces of H through its closed subgroups. We expose a detailed study on the control behavior (i.e., controllability property and control sets) of some particular dynamics evolving on non simply connected homogeneous (state) spaces of dimension two and three.