Structure preserving moment matching for port-Hamiltonian systems : Arnoldi and Lanczos

Structure preserving model reduction of single-input single-output port-Hamiltonian systems is considered by employing rational Krylov methods. The rational Arnoldi method is shown not only to preserve (for the reduced order model) 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. Index Terms: Reduced order systems, port-Hamiltonian systems, structure preservation, rational Krylov methods