Abstract:
The authors introduce and study a new concept—the absolute logarithmic norm—which has much in common with the classical definition of the logarithmic norms, according to S.M. Lozinsky. The developed theory allows to obtain new facts from the theory of Lyapunov stability for systems of linear differential equations with constant coefficients. The presentation of the material relies heavily on the theory undiagnosing nonnegative matrices arising from the theory of Perron–Frobenius for nonnegative matrices.
Keywords:logarithmic norm, Lyapunov stability, the theory of Perron–Frobenius for nonnegative matrices.
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