A note on the action of constant pseudostate feedback on the internal properness of an ARMA model

In this note we study the effect of constant pseudostate feedback on the internal properness of a linear multivariable system, described by an ARMA model. It is shown that the existence of a constant pseudostate feedback control law which makes the closed loop system internally proper is equivalent to the absence of decoupling zeros at infinity of the open loop system, a well known result from the theory of descriptor systems.