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Structure Preserving Moment Matching for Port-Hamiltonian Systems: Arnoldi and Lanczos

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2 Author(s)
Polyuga, R.V. ; ABM AMRO N.V. Bank, Amsterdam, Netherlands ; van der Schaft, A.

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.

Published in:

Automatic Control, IEEE Transactions on  (Volume:56 ,  Issue: 6 )