Title: Classification of controllable systems on low-dimensional solvable Lie groups
Authors: Yu.L. Sachkov
Journal title: Journal of Dynamical and Control Systems
Year: 2000
Volume: 6
Pages: 159—217
Abstract:

Right-invariant control systems on simply connected solvable Lie groups are studied. A complete and explicit description of controllable single-input right-invariant systems on such Lie groups up to dimension 6 is obtained.