This paper considers approximating a given nth-order stable transfer matrix G’s by an rth-order stable transfer matrix G(r)(s) in which n much greater than r, and where n is large, The Arnoldi process is used to generate a basis to a part of the controllability subspace associated with the realization of G(s), and a residual error is defined for any approximation in this subspace. We establish that minimizing the L-infinity norm of this residual error over the set of stable approximations leads to a 2-block distance problem. Finally, the solution of this distance problem is used to construct reduced-order approximate models. The behavior of the algorithms is illustrated with a simple example.