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Localization of eigenvalues of polynomial matrices

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Ukrainian Mathematical Journal Aims and scope

We consider the problem of localization of eigenvalues of polynomial matrices. We propose sufficient conditions for the spectrum of a regular matrix polynomial to belong to a broad class of domains bounded by algebraic curves. These conditions generalize the known method for the localization of the spectrum of polynomial matrices based on the solution of linear matrix inequalities. We also develop a method for the localization of eigenvalues of a parametric family of matrix polynomials in the form of a system of linear matrix inequalities.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv, Ukraine

    A. G. Mazko

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  1. A. G. Mazko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 8, pp. 1063–1077, August, 2010.

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Mazko, A.G. Localization of eigenvalues of polynomial matrices. Ukr Math J 62, 1234–1250 (2011). https://doi.org/10.1007/s11253-011-0426-y

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  • DOI: https://doi.org/10.1007/s11253-011-0426-y

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