Linear algebra of dissipative Hamiltonian systems.

Abstract: We will begin with a review of the Kronecker of pencils appearing in the port Hamiltonian modelling. Although the task seems to be completed by [1], and [2], the transfer function considerations in [3] put a different light on these results.

In the second part of the talk we will concentrate on the eigenvalue infinity, and the size of the largest Kronecker block - the index. We will study the perturbation properties of the eigenvalue infinity, presenting non-asymptotic results based on the Bauer-Fike theorem, see [4]. Several numerical examples will be considered.

[1] C. Mehl, V. Mehrmann, and M. Wojtylak. Matrix pencils with coefficients that have positive semidefinite Hermitian parts. SIMAX 2022.

[2] N. Gillis, V. Mehrmann, and P. Sharma. Computing the nearest stable matrix pairs. NLAA, 2018.

[3] K. Cherifi, H. Gernandt, and D. Hinsen. The difference between port-Hamiltonian, passive and positive real descriptor systems. MCSS, 2024.

[4] H. Blazhko, M. Wojtylak, Detection of the higher order Kronecker blocks by perturbation, 2026 , preprint.

mathematical physicsanalysis of PDEsdifferential geometrydynamical systemsfunctional analysisnumerical analysisoptimization and controlspectral theory

Audience: researchers in the discipline

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Port-Hamiltonian Seminar

Series comments: Slides and recordings can be found here: uni-wuppertal.sciebo.de/s/CQfBsXr9iOI17ZY

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