Verification of feedback linearizability conditions for control systems of the class C1

We consider the feedback linearizability problem for control systems of the class C
¹
with one-dimensional control, i.e., the problem of the existence of a change of variables of the class C and a change of the control of the class C
¹
which map a given nonlinear system to a linear one. We discuss conditions of feedback linearizability and give an algorithm for their verification.