Abstract
It is shown that no resonance and small time local controllability for an n-dimensional, real analytic, single input affine control system imply many standard necessary conditions for the existence of a continuous, asymptotically stabilizing (state) feedback control (ASFC). Furthermore, no resonance means there exist local coordinates in which the drift vector field is linear, yielding a canonical form for the study of sufficient conditions and construction of an ASFC. The roles of resonance and the Kawski necessary condition are examined in detail.
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