The construction of a canonical, or normal, representation for non-lin
ear systems, similar to the Morse canonical form in the linear case, i
s obtained. The problem considered consists, in particular, of studyin
g the existence of generalized transformations that achieve a desired
block decoupling. Such transformations generalize the notions of state
transformation, state feedback and output injection. A sufficient con
dition is given in terms of a separability condition, which in turn is
completely characterized by using differential forms and their proper
ties. (C) 1997 Elsevier Science Ltd.