Abstract
This paper is devoted to the study of global controllability of linear systems on higher dimensional Heisenberg groups . Necessary conditions and sufficient ones are provided. They are compared to the known necessary and sufficient conditions on stated in Dath and Jouan [(2016). Controllability of linear systems on low dimensional nilpotent and solvable Lie groups. Journal of Dynamical and Control Systems, 22(2), 207–225]. The notion of decoupled systems is introduced in order to get examples and counter-examples, and more precise controllability criteria are stated for them.
Disclosure statement
No potential conflict of interest was reported by the authors.
Notes
1 In other words the identity e should belong to an open subset of G included in the set of reachable points from e in time less than or equal to t with inputs uniformly bounded by B.
2 The derived subalgebras are defined inductively by and .
3 Because is a simply connected nilpotent Lie group.