Dispersiveness and controllability of invariant control systems on nilpotent Lie groups

This manuscript presents sufficient conditions for dispersiveness of invariant control systems on nilpotent Lie groups. The main theorem shows that a nilpotent control system is dispersive if its drift vector is not a linear combination of the controlled vectors and the Lie brackets among all the vector fields of the system. This condition implies a necessary condition for the existence of a control set. A classification of homogeneous and inhomogeneous nilpotent control systems is presented.