TY - JOUR
T1 - Weak condition for the existence of control sets with a nonempty interior for linear control systems on nilpotent groups
AU - Da Silva, Adriano
AU - Rojas, Anderson F.P.
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2024.
PY - 2025/3
Y1 - 2025/3
N2 - In this paper, we show that for a linear control system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior, as soon as one impose a compactness assumption on the generalized kernel of the drift. Moreover, this control set is unique and contains the singularities of the drift in its closure.
AB - In this paper, we show that for a linear control system on a nilpotent Lie group, the Lie algebra rank condition is enough to assure the existence of a control set with a nonempty interior, as soon as one impose a compactness assumption on the generalized kernel of the drift. Moreover, this control set is unique and contains the singularities of the drift in its closure.
KW - Control sets
KW - Linear control systems
KW - Nilpotent Lie groups
UR - https://www.scopus.com/pages/publications/85199330111
U2 - 10.1007/s00498-024-00395-4
DO - 10.1007/s00498-024-00395-4
M3 - Article
AN - SCOPUS:85199330111
SN - 0932-4194
VL - 37
SP - 61
EP - 79
JO - Mathematics of Control, Signals, and Systems
JF - Mathematics of Control, Signals, and Systems
IS - 1
ER -