Two theorems regarding the state-space realisation of the transfer-function matrix Z(s)
Mohammed I. Younis, William G. Vogt · Electronics Letters · 1966
This letter shows the independence of the matrix products (CAiB, i = 1, 2, …) from any state-space realisation of the infinite number of possible realisations1,2 of a transfer-function matrix Z (s). In addition, it shows that, in the sequnce (Z1, Z2, …) derived from Z(s), only the first M can be linearly independent, where M is the degree of the minimum polynomial of A.