Positivity preserving balanced truncation for descriptor systems
Please always quote using this URN:urn:nbn:de:0296-matheon-5258
- We propose a model reduction method for positive systems that ensures the positivity of the reduced-order model. In the standard as well as in the descriptor case, for 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. Positivity and stability are preserved and an error bound in the $\mathcal{H}_\infty$-norm is provided.
Author: | Elena Virnik, Timo Reis |
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URN: | urn:nbn:de:0296-matheon-5258 |
Referee: | Volker Mehrmann |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2008/04/09 |
Release Date: | 2008/02/09 |
Tag: | |
Institute: | Technische Universität Berlin |
MSC-Classification: | 34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Axx General theory / 34A09 Implicit equations, differential-algebraic equations [See also 65L80] |
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Bxx Controllability, observability, and system structure / 93B11 System structure simplification | |
Preprint Number: | 517 |