Controllability of linear systems on solvable lie groups

Linear systems on Lie groups are a natural generalization of linear systems on Euclidian spaces. For such systems, this paper studies controllability by taking into consideration the eigenvalues of an associated derivation D. When the state space is a solvable connected Lie group, controllability of the system is guaranteed if the reachable set of the neutral element is open and the derivation D has only pure imaginary eigenvalues. For bounded systems on nilpotent Lie groups such conditions are also necessary.