Generic nonlinear stabilization of systems with matching algebraic structure

The paper demonstrates that using algebraic methods for the construction of time varying stabilizing controls for general controllable systems which are affine in the control is not only computationally feasible, but delivers generic feedback laws. A single feedback control law can be stabilizing for all systems which have the same algebraic structure and also for systems that can be adequately approximated by this structure. The systems considered are not limited to those whose controllability Lie algebra is nilpotent or even finite dimensional. The stabilizing controls are constructed by the help of an open-loop control problem on an associated Lie group which is posed as a trajectory interception problem in the logarithmic coordinates of flows.