Exponential Stabilization of Driftless Nonlinear Control Systems via Time-varying, Homogeneous Feedback

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Robert T. M'Closkey and Richard M. Murray
Proceedings of the 32nd Conference on Decision and Control
December 1994

This paper brings together results from a number of different areas in control theory to provide an algorithm for the synthesis of locally exponentially stabilizing control laws for a large class of driftless nonlinear control systems. The exponential stabilization relies on the use of feedbacks which render the closed loop vector field homogeneous with respect to a dilation. These feedbacks are generated from a modification of Pomet's algorithm for smooth feedbacks. Converse Liapunov theorems for time-periodic homogeneous vector fields guarantee that local exponential stability is maintained in the presence of higher order (with respect to the dilation) perturbing terms.