Boundedness control sets for linear systems on Lie groups

Abstract

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

Keywords

• decomposable group
• linear system
• control set
• boundedness
• 16w25
• 93b05
• 93c05