Rational matrix approximation with a priori error bounds for non-symmetric matrix Riccati equations with analytic coefficients

In this paper the exact solution of the non-symmetric matrix Riccati equation with analytic coefficients is approximated by a rational matrix function with a prefixed accuracy. This rational matrix function is locally defined as the exact solution of a Riccati problem with matrix polynomial coefficients obtained by truncation of the Taylor expansions of the matrix coefficients of the original problem.