Time varying stabilizing feedback for drift free systems via optimization on a Lie group

A method is presented for construction of time varying stabilizing feedback control for systems without drift. The method is universal in the sense that it is independent of the vector fields determining the motion of the system, or of the choice of a Lyapunov function. The proposed feedback law is a composition of a standard stabilizing feedback control for a Lie bracket extension of the original system and a periodic continuation of a specific solution to an open loop control problem on the associated Lie group. The latter is posed as a feasibility or optimal control problem in the Philip Hall coordinates of flows