  We investigate a new class of nonlinear control systems of O.D.E., which are
not feedback linearizable in general. Our class is a generalization of the
well-known feedback linearizable systems, and moreover it is a generalization
of the triangular (or pure-feedback) forms studied before. The definition of
our class is global, and coordinate-free, which is why the problem of the
equivalence is solved for our class in the whole state space at the very
beginning. The goal of this paper is to prove the global controllability of our
nonlinear systems. We propose to treat our class as a new canonical form which
is a nonlinear global analog of the Brunovsky canonical form on the one hand,
and is a global and coordinate-free generalization of the triangular form on
the other hand.
