Model reduction via truncation: an interpolation point of view

In this paper, we focus our attention on linear time invariant continuous time linear systems with one input and one output (SISO LTI systems). We consider the problem of constructing a reduced order system via truncation of the original system. Given a SISO strictly proper transfer function T(s) of McMillan degree N and a strictly proper SISO transfer function (T) over cap (s) of McMillan degree n < N, we prove that (T) over cap (s) can always be constructed via truncation of the system T(s). The proof is mainly based on interpolation theory, and more precisely on multipoint Pade interpolation. Moreover, new results about Krylov subspaces are developed. (C) 2003 Elsevier Inc. All rights reserved.