EXPONENTIAL STABILIZATION OF DRIFTLESS NONLINEAR CONTROL-SYSTEMS USING HOMOGENEOUS FEEDBACK

This paper focuses on the problem of exponential stabilization of cont rollable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nons tandard dilation that is compatible with the algebraic structure of th e control Lie algebra. It can be shown that any continuous, time-varyi ng controller that achieves exponential stability relative to the Eucl idean norm is necessarily non-lipschitz, Despite these restrictions, w e provide a set of constructive, sufficient conditions for extending s mooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from th e 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 stabi lizers.