Structure, Smith-MacMillan form and coprime MFDs of a rational matrix inside a region P =ω∪{∞}

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Abstract
The structure of the Smith-MacMillan form of a rational matrix T(s) inside a region P=ω∪{∞} (where ω is asymmetric with respect to the real axis subset of the finite complex plane C) is determined. Algorithmic procedures based on elementary row and column operations over the euclidean ring R P(s) consisting of all rational functions with no poles in P are given. Coprimeness in P of a pair of rational matrices is studied in detail. These results lead to constructive procedures for determining the coprime in P matrix fraction descriptions of T(a).