This paper focuses on the problem of exponential stabilization of
controllable, driftless systems using time-varying, homogeneous
feedback. The analysis is performed with respect to a homogeneous
norm in a non-standard dilation that is compatible with the algebraic
structure of the control Lie algebra. Using this structure, we show
that any continuous, time-varying controller that achieves exponential
stabilization relative to the Euclidean norm is necessarily
non-Lipschitz. Despite these restrictions, we provide a set of
constructive, sufficient conditions for extending smooth, asymptotic
stabilizers to homogeneous, exponential stabilizers. The modified
feedbacks are everywhere continuous, smooth away from the origin, and
can be extended to a large class of systems with torque inputs. The
feedback laws are applied to an experimental mobile robot and show
significant improvement in convergence rate over smooth stabilizers
