Homogeneous feedback laws in dimension three

Consideration is given to single-input systems on R/sup 3/ that are small-time locally controllable. The inherent symmetries of the standard nilpotent approximations to such systems are used to show how to construct Holder continuous feedback laws that respect the symmetries and asymptotically stabilize the control system. An explicit example is worked in detail, and a necessary condition for the existence of such stabilizing feedback laws is obtained.<>