Preprint No. MPIMD/14-11

Title: Positive Operators and Stable Truncation

Author(s): Peter Benner, Tobias Damm, Martin Redmann, Yolanda Rocio Rodriguez Cruz


Date: 2014-07-05


We introduce a notion of balanced truncation for generalized Lyapunov operators and show that it preserves asymptotic stability. The proof relies on the theory of positive mappings and a result by Hans Schneider. Applications of our result can be found in model order reduction of stochastic linear systems.


author = {Peter Benner and Tobias Damm and Martin Redmann and Yolanda Rocio Rodriguez Cruz},
title = {Positive Operators and Stable Truncation},
number = {MPIMD/14-11},
month = jul,
year = 2014,
institution = {Max Planck Institute Magdeburg},
type = {Preprint},
note = {Available from \url{}},

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