Boundedness control sets for linear systems on Lie groups

Let be a linear system on a connected Lie group and assume that the reachable set A from the identity element ∈ is open. In this paper, we give an algebraic condition to warrant the boundedness of the existent control set with a nonempty interior containing . We concentrate the search for the class of decomposable groups which includes any solvable group and also every compact semisimple group.