Time-varying stabilization of a class of driftless systems satisfying second-order controllability conditions

In this paper, we propose a stabilization scheme for nonlinear control systems whose vector fields satisfy Hormander's condition with the second-order Lie brackets. This scheme is based on the use of trigonometric controls with bounded frequencies. By using the Volterra series and a modification of Lyapunov's direct method, we reduce the stabilization problem to a system of cubic equations and prove its local solvability. Our approach ensures exponential stability of the equilibrium and gives explicit formulas for the coefficients of the control functions. The proposed methodology is illustrated by a rolling disc example.