Symmetric Positivity Preserving Balanced Truncation

Abstract

We consider positivity preserving model order reduction of SISO linear systems. Whereas well‐established model reduction methods usually do not result in a positive approximation, we show that a symmetry characterization of balanced truncation can be used to preserve positivity after performing balanced truncation. As a consequence, the method is independent of the initial realization and always returns a symmetric reduced model. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)