This article is cited in 4 papers

On the Construction of Stability Indicators for Nonnegative Matrices

V. N. Razzhevaikin^a, E. E. Tyrtyshnikov<sup>b

a</sup> Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, Moscow
^b Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow

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 to use 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.

Keywords: nonnegative matrix, stability indicator.

UDC: 519.614.2

Received: 06.05.2020
Revised: 19.10.2020

DOI: 10.4213/mzm12782

 English version: Mathematical Notes, 2021, 109:3, 435–444

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