Structure preserving model reduction of port-Hamiltonian systems by moment matching at infinity

Authors:
Rostyslav V. Polyuga;Arjan van der Schaft
Affiliations:
Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands;Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen, The Netherlands
Venue:
Automatica (Journal of IFAC)
Year:
2010

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Abstract

Model reduction of port-Hamiltonian systems by means of the Krylov methods is considered, aiming at port-Hamiltonian structure preservation. It is shown how to employ the Arnoldi method for model reduction in a particular coordinate system in order to preserve not only a specific number of the Markov parameters but also the port-Hamiltonian structure for the reduced order model. Furthermore it is shown how the Lanczos method can be applied in a structure preserving manner to a subclass of port-Hamiltonian systems which is characterized by an algebraic condition. In fact, for the same subclass of port-Hamiltonian systems the Arnoldi method and the Lanczos method turn out to be equivalent in the sense of producing reduced order port-Hamiltonian models with the same transfer function.