Structured Backward Errors for Eigenvalues of Linear Port-Hamiltonian Descriptor Systems
(2021) SIAM Journal on Matrix Analysis and Applications — Vol. 42, n° 1, p. 1-16 (2021)
Files
MehrmannV20c.pdf
Open Access - Adobe PDF
- 368.94 KB
Details
- Authors
Van Dooren, Paul 
- 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.
- Affiliations
Citations
Mehrmann, V., & Van Dooren, P. (2021). Structured Backward Errors for Eigenvalues of Linear Port-Hamiltonian Descriptor Systems. SIAM Journal on Matrix Analysis and Applications, 42(1), 1-16. https://doi.org/10.1137/20m1344184 (Original work published 2021)