On Parametrization of All the Exact Pole-Assignment State-Feedbacks for LTI Systems

In this technical note, we provide a parametrization of all the exact pole-assignment state-feedbacks for LTI systems, when the set of poles to be assigned contains sufficient number of real eigenvalues. We also refute a recent conjecture concerning the explicit form of all the state-feedbacks assigning a given set of poles to the closed-loop.