On Linearization of Single-Input Nonlinear Control Systems Based on Time Scaling and a One-Fold Prolongation

We prove a necessary and sufficient condition for the linearizability of single-input nonlinear control systems in the class of transformations containing time scaling and preserving the state manifold. A description is given for systems that are obtained by a 1-fold prolongation of a single-input nonlinear control system and are A-orbitally linearizable. It is proved that the A-orbital linearizability of the system obtained by a 1-fold prolongation of a single-input affine control system implies the A-orbital linearizability of the original system as well. It is shown that if the system obtained by a k-fold prolongation of a single-input nonlinear control system, where k = 2, is A-orbitally linearizable, then the system obtained from the original system by its 1-fold prolongation is A-orbitally linearizable as well.