Exponential Stabilization of Driftless Nonlinear Control Systems via Time-varying, Homogeneous Feedback
Robert T. M'Closkey and Richard M. Murray
Proceedings of the 32nd Conference on Decision and Control
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.
- Conference paper: http://www.cds.caltech.edu/~murray/preprints/mm94-cdc.pdf