Controllability of linear systems on lie groups with finite semi simple center

This paper studies controllability for a given linear system Σ on a connected Lie group G by taking into consideration the eigenvalues of an associated derivation D. If we assume that the Lie group G has finite center and, for some τ > 0, the identity element of G is an interior point of its reachable set at time τ, then the system is controllable if D has only eigenvalues with zero real part.