On the use of functional models in model reduction

Abstract

It has been known for some time that the Sylvester equation plays a significant role in interpolation, feedback control, observer theory and model reduction problems. In this paper, in place of state space techniques, we use polynomial models to replace the standard Sylvester equation by a polynomial version. The polynomial Sylvester equation is closely related to a Bezout equation. We use this functional setting to unify various model reduction techniques. © 2010 Springer-Verlag Berlin Heidelberg.