A generalized triangular form and its global controllability
  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. 
Svyatoslav S. Pavlichkov