On A-Orbital Linearization of Three-Dimensional Single-Input Affine Systems

The problem of A-orbital linearization of nonlinear control-affine systems is considered. Under the currently known conditions for A-orbital linearizability, it is assumed that the C-infinity-module generated by the vector fields corresponding to the system has constant rank. In the present paper, this assumption is dropped. A necessary and sufficient local condition is proved under which a three-dimensional single-input affine system is A-orbitally feedback and state equivalent to a linear controllable system considered in a neighborhood of an equilibrium.