No abstract

This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups.Some general necessary controllability conditions and some sufficient ones are provided.We introduce the notion of decoupled systems, and more precise controllability criteria are stated for them. The system Lie algebra and the rank conditionLet V stand for the subspace of g generated by {B 1 , . . . , B m }, let us denote by DV the smallest D-invariant subspace of g that contains V , i.e. DV = Span{D k Y ; Y ∈ V and k ∈ N}, and let LA(DV ) be the g subalgebra generated by DV (as previously D = −ad(X )).Proposition 1 The subalgebra LA(DV ) of g is D-invariant. It is therefore equal to the zero-time ideal L 0 , and the system Lie algebra L is equal toThe rank condition is satisfied by (Σ) if and only if L 0 = g.

No abstract