Design of Homogeneous Time-Varying Stabilizing Control Laws for Driftless Controllable Systems Via Oscillatory Approximation of Lie Brackets In closed-loop
Résumé
A constructive method for time-varying stabilization of smooth driftless controllable systems is developed. It provides time-varying homogeneous feedback laws that are continuous and smooth away from the origin. These feedbacks render the closed-loop system globally exponentially asymptotically stable if the driftless controllable system under consideration is homogeneous with respect to a certain family of dilations, and locally exponentially asymptotically stable, using local homogeneous approximation of control systems, in the other case. The method uses some known algorithms that construct oscillatory control inputs to approximate motion along Lie brackets. These algorithms have to be adapted to the closed-loop context.