Structured backward errors for eigenvalues of linear port-Hamiltonian descriptor systems

Volker Mehrmann; Paul Van Dooren

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arXiv · 2005.04744

Structured backward errors for eigenvalues of linear port-Hamiltonian descriptor systems

Volker Mehrmann·Paul Van Dooren

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Abstract

When computing the eigenstructure of matrix pencils associated with the passivity analysis of perturbed port-Hamiltonian descriptor system using a structured generalized eigenvalue method, one should make sure that the computed spectrum satisfies the symmetries that corresponds to this structure and the underlying physical system. We perform a backward error analysis and show that for matrix pencils associated with port-Hamiltonian descriptor systems and a given computed eigenstructure with the correct symmetry structure there always exists a nearby port-Hamiltonian descriptor system with exactly that eigenstructure. We also derive bounds for how near this system is and show that the stability radius of the system plays a role in that bound.

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Volker Mehrmann, Paul Van Dooren. 2020-05-10. Structured backward errors for eigenvalues of linear port-Hamiltonian descriptor systems. https://arxiv.org/abs/2005.04744

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