Structural conditions for disturbances decoupling with stability using proportional and derivative control laws

We consider the disturbance decoupling problem with internal stability by means of generalized control laws which use not only state feedback, but also external terms coming from the disturbance and some of its time derivatives. We derive from our previous geometric condition an equivalent one in terms of some structures of the system to be controlled (zeros at infinity and unstable zeros), and no longer dependent on a particular approach (geometric, algebraic, ...).