Some conclusions on the controllability of linear systems over F(z) in frequency domain

In this paper, the concepts of unimodular matrix and co-primeness of the polynomial matrix over the ring of F(z)[s] are defined. PBH (Popov-Belevich-Hautus) controllability criterion for the system over F(z) is stated. An illustrative example is given and the controllability conditions of a class of RFS (Rational Function Systems) are proven. The sufficient and necessary controllability conditions of composite linear system over F(z) in frequency domain are discussed. Some conditions are extensions of the well-known results of linear systems over R in frequency domain.