Controllability canonical (phase-variable) form for non-linear time-variable systems

A controllability canonical form for non-linear time-variable systems with a control variable appearing linearly is introduced. The global controllability of this nonlinear phase-variable form is given independently of the non-linearities. A transformation to the controllability canonical form requires the regularity of a matrix which can be considered the controllability matrix of a non-linear time-variable system. A problem which still remains unsolved is the actual computation of the non-linear controllability canonical form for a given system.