Absolute Logarithmic Norm

Absolute Logarithmic Norm

In this paper we introduce and study a new concept of the absolute logarithmic norm, which has much in common with the classical definition of the logarithmic norm by S. M. Lozinskii. The the theory that we develop allows to obtain new facts from the Lyapunov stability theory for the systems of line...

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Veröffentlicht in:Russian mathematics 2018-04, Vol.62 (4), p.60-73
Hauptverfasser: Perov, A. I., Kostrub, I. D., Kleshchina, O. I., Dikarev, E. E.
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Differential equations
Mathematics
Mathematics and Statistics
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container_end_page 73
container_issue 4
container_start_page 60
container_title Russian mathematics
container_volume 62
creator Perov, A. I.
Kostrub, I. D.
Kleshchina, O. I.
Dikarev, E. E.
description In this paper we introduce and study a new concept of the absolute logarithmic norm, which has much in common with the classical definition of the logarithmic norm by S. M. Lozinskii. The the theory that we develop allows to obtain new facts from the Lyapunov stability theory for the systems of linear differential equations with constant coefficients. The presentation of the material relies heavily on the theory of off-diagonally nonnegative matrices arising from the Perron–Frobenius theory for nonnegative matrices.
doi_str_mv 10.3103/S1066369X18040072
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subjects Differential equations
Mathematics
Mathematics and Statistics
title Absolute Logarithmic Norm
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