We study controllability of right-invariant control systems 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 . As an application, right-invariant systems on metabelian groups and matrix groups, and bilinear systems are considered.
Title: Controllability of Right-Invariant Systems on Solvable Lie Groups
Authors: Yu. L. Sachkov
Journal title: Journal of Dynamical and Control Systems