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Benner, Peter ; Damm, Tobias:
Lyapunov Equations, Energy Functionals, and Model Order Reduction of Bilinear and Stochastic Systems.
In: SIAM Journal on Control and Optimization.
Bd. 49
(2011)
Heft 2
.
- S. 686-711.
ISSN 1095-7138
DOI: https://doi.org/10.1137/09075041X
Abstract
We discuss the relation of a certain type of generalized Lyapunov equations to Gramians of stochastic and bilinear systems together with the corresponding energy functionals. While Gramians and energy functionals of stochastic linear systems show a strong correspondence to the analogous objects for deterministic linear systems, the relation of Gramians and energy functionals for bilinear systems is less obvious. We discuss results from the literature for the latter problem and provide new characterizations of input and output energies of bilinear systems in terms of algebraic Gramians satisfying generalized Lyapunov equations. In any of the considered cases, the definition of algebraic Gramians allows us to compute balancing transformations and implies model reduction methods analogous to balanced truncation for linear deterministic systems. We illustrate the performance of these model reduction methods by showing numerical experiments for different bilinear systems.
Weitere Angaben
| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Zusätzliche Informationen: | Zentralblattnummer: pre05931218 |
| Keywords: | Lyapunov equations; Gramians; energy functionals; balanced truncation; model order reduction; bilinear systems; stochastic systems |
| Fachklassifikationen: | Mathematics Subject Classification Code: 93A15 (93A30 93C10 93E20 93B40) |
| Institutionen der Universität: | Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut |
| Titel an der UBT entstanden: | Nein |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 03 Mär 2021 13:35 |
| Letzte Änderung: | 23 Mär 2021 09:12 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/63653 |