On the extension of the Korobov's class of linearizable triangular systems by nonlinear control systems of the class C1

We give the complete description of nonlinear control systems of the class C1 with one-dimensional control which are feedback linearizable by means of a change of the control of the class C1 and a change of variables of the class C2 as well as the control systems which are linearizable by means of a change of variables only. The both results are originated from the approach proposed by V.I. Korobov in 1973 for the linearization of triangular control systems.