Abstract
We analyse and construct the matrix-valued proper rational solutions of the tangential interpolation problem. We show how the coprime polynomial factorization of the solutions is tightly connected to the controllability indices of a pair $$({\mathscr {A}},[U,V])$$ associated with the interpolation data and that coprimeness of these factorizations is guaranteed by a simple condition on the eigenvectors of $${\mathscr {A}}$$ .
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