On multivariable proper rational interpolation using coprime factors

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 (A,[U,V])\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$({\mathscr {A}},[U,V])$$\end{document} associated with the interpolation data and that coprimeness of these factorizations is guaranteed by a simple condition on the eigenvectors of A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {A}}$$\end{document}.