On classical solutions in the stabilization problem for nonholonomic control systems with time-varying feedback laws

We consider the stabilization problem for driftless control-affine systems under the bracket-generating condition. In our previous works, a class of time-varying feedback laws has been constructed to stabilize the equilibrium of a nonholonomic system under rather general controllability assumptions. This stabilization scheme is based on the sampling concept, which is not equivalent to the classical definition of solutions for the corresponding nonautonomous closed-loop system. In the present paper, we refine the previous results by presenting sufficient conditions for the convergence of classical solutions of the closed-loop system to the equilibrium. Our theoretical findings are applied to a multidimensional driftless control-affine system and illustrated through numerical simulations.