Canonical realizations by factorization of constant matrices

In van der Schaft and Rapisarda (2011) [3] we showed that a state variable for a LTI system can be computed factorizing a two-variable polynomial matrix computed directly from the system equations. Different factorizations of this matrix yield different state maps, and consequently different state equations; based on this fact we present a unifying point of view on some classical canonical forms for linear systems.