%0 Journal Article %1 Polyuga2011Structure %A Polyuga, Rostyslav V. %A van der Schaft, Arjan %D 2011 %J IEEE Transactions on Automatic Control %K 00a71-theory-of-mathematical-modeling 37j05-finite-dimensional-hamiltonian-general-theory 41a35-approximation-by-operators-in-particular-integral-operators %N 6 %P 1458--1462 %R 10.1109/tac.2011.2128650 %T Structure Preserving Moment Matching for Port-Hamiltonian Systems: Arnoldi and Lanczos %U http://dx.doi.org/10.1109/tac.2011.2128650 %V 56 %X Structure preserving model reduction of single-input single-output port-Hamiltonian systems is considered by employing the rational Krylov methods. The rational Arnoldi method is shown to preserve (for the reduced order model) not only a specific number of the moments at an arbitrary point in the complex plane but also the port-Hamiltonian structure. Furthermore, it is shown how the rational Lanczos method applied to a subclass of port-Hamiltonian systems, characterized by an algebraic condition, preserves the port-Hamiltonian structure. In fact, for the same subclass of port-Hamiltonian systems the rational Arnoldi method and the rational Lanczos method turn out to be equivalent in the sense of producing reduced order port-Hamiltonian models with the same transfer function.

@article{Polyuga2011Structure, abstract = {{Structure preserving model reduction of single-input single-output port-Hamiltonian systems is considered by employing the rational Krylov methods. The rational Arnoldi method is shown to preserve (for the reduced order model) not only a specific number of the moments at an arbitrary point in the complex plane but also the port-Hamiltonian structure. Furthermore, it is shown how the rational Lanczos method applied to a subclass of port-Hamiltonian systems, characterized by an algebraic condition, preserves the port-Hamiltonian structure. In fact, for the same subclass of port-Hamiltonian systems the rational Arnoldi method and the rational Lanczos method turn out to be equivalent in the sense of producing reduced order port-Hamiltonian models with the same transfer function.}}, added-at = {2019-03-01T00:11:50.000+0100}, author = {Polyuga, Rostyslav V. and van der Schaft, Arjan}, biburl = {https://www.bibsonomy.org/bibtex/2fdb08ab56514cab9b8198145e6dfe7af/gdmcbain}, citeulike-article-id = {14497240}, citeulike-attachment-1 = {polyuga_11_structure.pdf; /pdf/user/gdmcbain/article/14497240/1124205/polyuga_11_structure.pdf; 3ca9903dc666a8501b12907fb6d18ae08dd87f83}, citeulike-linkout-0 = {http://dx.doi.org/10.1109/tac.2011.2128650}, doi = {10.1109/tac.2011.2128650}, file = {polyuga_11_structure.pdf}, interhash = {c52aa411e14ba862156e30f3e1df1271}, intrahash = {fdb08ab56514cab9b8198145e6dfe7af}, issn = {0018-9286}, journal = {IEEE Transactions on Automatic Control}, keywords = {00a71-theory-of-mathematical-modeling 37j05-finite-dimensional-hamiltonian-general-theory 41a35-approximation-by-operators-in-particular-integral-operators}, month = jun, number = 6, pages = {1458--1462}, posted-at = {2017-12-05 23:54:31}, priority = {5}, timestamp = {2019-03-01T00:11:50.000+0100}, title = {{Structure Preserving Moment Matching for Port-Hamiltonian Systems: Arnoldi and Lanczos}}, url = {http://dx.doi.org/10.1109/tac.2011.2128650}, volume = 56, year = 2011 }