On one stability criterion for linear systems of differential equations with periodic coefficients

To check stability in linear systems of differential equations with periodic coefficients, we use a weighted Lozinski logarithmic norm. As the weights, we propose to take positive components of the Perron eigenvector for a constant off‐diagonally nonnegative matrix that results by averaging the original system with diagonal elements replaced by their real parts and all off‐diagonal coefficients replaced by their absolute values.