Positivity preserving balanced truncation
Please always quote using this URN:urn:nbn:de:0296-matheon-4269
- We propose a model reduction method for positive systems that ensures the positivity of the reduced model. For both, continuous-time and discrete-time systems, our approach is based on constructing diagonal solutions of Lyapunov inequalities. These are linear matrix inequalities (LMIs), which are shown to be feasible. Stability is preserved and an error bound in the $\mathcal{H}_\infty$-norm is provided.
Author: | Timo Reis, Elena Virnik |
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URN: | urn:nbn:de:0296-matheon-4269 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2007/08/11 |
Release Date: | 2007/06/11 |
Tag: | |
Institute: | Technische Universität Berlin |
MSC-Classification: | 15-XX LINEAR AND MULTILINEAR ALGEBRA; MATRIX THEORY / 15Axx Basic linear algebra / 15A39 Linear inequalities |
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Mxx Approximation methods and numerical treatment of dynamical systems [See also 65Pxx] / 37M99 None of the above, but in this section | |
37-XX DYNAMICAL SYSTEMS AND ERGODIC THEORY [See also 26A18, 28Dxx, 34Cxx, 34Dxx, 35Bxx, 46Lxx, 58Jxx, 70-XX] / 37Nxx Applications / 37N35 Dynamical systems in control | |
Preprint Number: | 414 |