On Singularities of $$A$$-Orbital Feedback Linearization of Single-InputAffine Controllable Systems

For single-input affine control systems, we address the problem of $$A $$ -orbital feedback linearization around singular points of the derived flag of the distribution associated with the control system. By a singular point of a derived flag we mean a point such that at least one of the elements of the derived flag in any neighborhood of this point is not a distribution of constant rank. We prove a local necessary and sufficient condition for A-orbital feedback equivalence of a single-input affine control system to a linear controllable system considered in a neighbourhood of the zero equilibrium point.