| A linear control system ∑ on a Lie group G is defined by x&d2;=Xx +j=1ujY jx, where the drift vector field X is an infinitesimal automorphism, uj are piecewise constant functions, and the control vectors Yj are left-invariant vector fields. In this work, properties for the flow of the infinitesimal automorphism X and for the reachable set defined by ∑ are presented. Under a condition similar to the Kalman condition which is needed for controllability of linear control systems on , the system ∑ is locally controllable at the group identity e. A proof of this result is obtained using Lie theory of semigroups. More importantly, an extension of this result is proved. Finally, an example on the Heisenberg Lie group is presented and its properties are proved using the theory developed. |