Scientific articles

Hurwitz matrix, Lyapunov and Dirichlet on the sustainability of Lyapunov’s

I. D. Kostrub

Voronezh State University

Abstract: The concepts of Hurwitz, Lyapunov and Dirichlet matrices are introduced for the convenience of the stability of linear systems with constant coefficients. They allow us to describe all the cases of interest in the stability theory of linear systems with constant coefficients. A similar classification is proposed for systems of linear differential equations with periodic coefficients. Monodromy matrices of such systems can be either Hurwitz matrices or Lyapunov matrices or Dirichlet matrices (in the discrete sense) in a stable case. The new material relates to systems with variable coefficients.

Keywords: stability of linear systems with constant, periodic coefficients, Hurwitz, Lyapunov and Dirichlet matrices, classification of monodromy matrices.

UDC: 517.925

Received: 22.04.2018

DOI: 10.20310/1810-0198-2018-23-123-431-436

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