Doubly coprime decompositions of a collection of rational matrices

An N-periodic discrete-time system in z-domain given by an N-periodic collection of rational matrices is considered. Doubly coprime decomposition of these matrices is studied. For such decompositions, the block-ordered concept is used. Further, the eight matrices in the generalized Bezout identity, so that all of them are block-ordered, can be chosen. A relation among these matrices at consecutive times is established.