  A system is Koopman super-linearizable if it admits a finite-dimensional
embedding as a linear system. Super-linearization is used to leverage methods
from linear systems theory to design controllers or observers for nonlinear
systems. We call a super-linearization balanced if the degrees of the hidden
observables do not exceed the ones of the visible observables. We show that
systems admitting such super-linearization can be put in a simple canonical
form via a linear change of variables.
