Minimal stabilizers with arbitrary spectrum for SIMO and MISO systems

We consider two classes of linear dynamical systems, single-input-many-output (SIMO) systems and many-input-single-output (MISO) systems. For both classes, we consider the problem of synthesizing a stabilizer of minimum dimension providing pole assignment in the closed-loop system. We show that, for these classes, a minimal stabilizer providing pole assignment has dimension k _min = min{ν ? 1, µ ? 1}, where ν and µ are the controllability and observability indices of the original (SIMO or MISO) dynamical system.