  In this paper, we study transfer functions corresponding to parametric linear
systems whose coefficients are block matrices. Thus, these transfer functions
constitute Laurent polynomials whose coefficients are square matrices. We
assume that block matrices defining the parametric linear systems are solutions
of an integrable hierarchy called for us, the block matrices version of the
finite discrete KP hierarchy, which is introduced and studied with certain
detail in this paper. We see that the linear system defined by means of the
simplest solution of the integrable system is controllable and observable.
  Then, as a consequence of this fact, it is possible to verify that any
solution of the integrable hierarchy, obtained by the dressing method of the
simplest solution, defines a parametric linear system which is also
controllable and observable.
