Coprime factorizations in stable linear systems
A block-diagonal linear (not necessarily time-invariant) map P with a right-coprime factorization ND-1 (or a left-coprime factorization D-1N) is considered. It is shown that the individual blocks in P have right-coprime factorizations (left-coprime factorizations, respectively) if and only if the denominator map D has a special block-triangular structure. This condition is applied to the stable linear feedback system S(P1,P2).
Desoer, Charles A.↗