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

Abstract

Abstract: The problem of A-orbital linearizationof nonlinear control-affine systems is considered. Under the currently known conditions for A-orbital linearizability, it is assumed that the C∞-module generated by the vector fieldscorresponding 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-inputaffine system is A-orbitally feedback and state equivalent to a linearcontrollable system considered in a neighborhood of an equilibrium.