Title: Controllability of Right-Invariant Systems on Solvable Lie Groups
Authors: Yu. L. Sachkov
Journal title: Journal of Dynamical and Control Systems
Year: 1997
Volume: 3
Pages: 531—564
Abstract:

We study controllability of right-invariant control systems $$\Gamma = A + R \ B$$ on Lie groups. Necessary and sucient controllability conditions for Lie groups not coinciding with their derived subgroup are obtained in terms of the root decomposition corresponding to the adjoint operator $$ad\ B$$. As an application, right-invariant systems on metabelian groups and matrix groups, and bilinear systems are considered.