On the derivation of a state-space model of a periodic process described by recurrent equations

where T(6), U(6), V(6) and W(6) are polynomial matrices in the indeterminate 6, which for recurrent equations can have the meaning of the one-step forward-shift operator. He showed that under the polynomial transformations on (1.1), (1.2) that he called strict system equivalence, if T(6) is square, detT(6) ^ 0 (and has a degree equal to the dimension of T(6)) and the input-output transfer matrix corresponding to (1.1), (1.2) is proper, then it is possible to obtain a description of the same process in state-space form, i.e., in the case of recurrent equations, of the type