Russian Mathematics

, Volume 62, Issue 4, pp 60–73 | Cite as

Absolute Logarithmic Norm

  • A. I. Perov
  • I. D. Kostrub
  • O. I. Kleshchina
  • E. E. Dikarev


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.


logarithmic norm Lyapunov stability the theory of Perron–Frobenius for nonnegative matrices 


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Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  • A. I. Perov
    • 1
  • I. D. Kostrub
    • 1
  • O. I. Kleshchina
    • 1
  • E. E. Dikarev
    • 1
  1. 1.Voronezh State UniversityVoronezhRussia

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