Para-Hermitian Rational Matrices
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Date
2024
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Mcode
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Language
en
Pages
21
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SIAM Journal on Matrix Analysis and Applications, Volume 45, issue 4, pp. 2339-2359
Abstract
In this paper, we study para-Hermitian rational matrices and the associated structured rational eigenvalue problem (REP). Para-Hermitian rational matrices are Square rational matrices that are Hermitian for all z on the unit circle that are not poles. REPs are often solved via linearization, that is, using matrix pencils associated to the corresponding rational matrix that preserve the spectral structure. Yet, nonconstant polynomial matrices cannot be para-Hermitian. Therefore, given a para-Hermitian rational matrix R(z), we instead construct a *-palindromic linearization for (1 -\- z)R(z), whose eigenvalues that are not on the unit circle preserve the symmetries of the zeros and poles of R(z). This task is achieved via Möbius transformations. We also give a constructive method that is based on an additive decomposition into the stable and antistable parts of R(z). Analogous results are presented for para-skew-Hermitian rational matrices, i.e., rational matrices that are skew-Hermitian upon evaluation on those points of the unit circle that are not poles.Description
Publisher Copyright: Copyright © by SIAM.
Keywords
*-palindromic, linear System matrices, linearization, Mobius, para-Hermitian, rational matrices, strong minimality
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Citation
Dopico, F M, Noferini, V, Quintana, M C & van Dooren, P 2024, ' Para-Hermitian Rational Matrices ', SIAM Journal on Matrix Analysis and Applications, vol. 45, no. 4, pp. 2339-2359 . https://doi.org/10.1137/24M1678416