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On the Construction of Stability Indicators for Nonnegative Matrices

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Abstract

Given a square nonnegative matrix \(A\), a simple algorithm is suggested for constructing a stability indicator characterizing the localization of its spectrum in the unit disk. Theorems are proved which establish the possibility of using the maximum of \(1-\det(I-J)\) over all possible principal submatrices \(J\) of \(A\) as a suitable indicator and give conditions under which such a maximum can be calculated only over a certain chain of leading principal submatrices. Applied problems that need such constructions and a relationship between the obtained results and similar results established for a number of matrices of special form are considered.

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Funding

This work was financially supported by the Russian Science Foundation under grant 19-11-00338.

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Authors and Affiliations

  1. Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, Moscow, 119333, Russia

    V. N. Razzhevaikin

  2. Marchuk Institute of Numerical Mathematics of Russian Academy of Sciences, Moscow, 119991, Russia

    E. E. Tyrtyshnikov

Authors
  1. V. N. Razzhevaikin
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  2. E. E. Tyrtyshnikov
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Corresponding author

Correspondence to V. N. Razzhevaikin.

Additional information

Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 407-418 https://doi.org/10.4213/mzm12782.

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Razzhevaikin, V.N., Tyrtyshnikov, E.E. On the Construction of Stability Indicators for Nonnegative Matrices. Math Notes 109, 435–444 (2021). https://doi.org/10.1134/S0001434621030111

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  • DOI: https://doi.org/10.1134/S0001434621030111

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