A note on the action of constant pseudostate feedback on the internal properness of an ARMA model (Q1304043)

The effect of constant pseudostate feedback on the internal properties of a linear multivariable system described by an ARMA model is studied. It is shown that a necessary and sufficient condition for the existence of an admissible pseudostate feedback such that the closed-loop system is internally proper is the absence of decoupling zeros at infinity in the open-loop system. This condition looks like a generalization of known results from the theory of descriptor systems and particularly the ones regarding the impulsive controllability of a generalized state space system.