A version of the Floquet theory for first order delay differential equations is proposed. Formula of solutions representation is obtained. On this basis, the stability of first order delay differential equations is studied. An analogue of the classical integral Lyapunov–Zhukovskii test of stability is proved. New, in comparison with all known, tests of the exponential stability are obtained on the basis of the Floquet theory. A possibility to achieve the exponential stability is connected with oscillation of solutions.

中文翻译：

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一类时滞一阶微分方程的Floquet理论与稳定性

提出了用于一阶时滞微分方程的 Floquet 理论的一个版本。得到解的表示公式。在此基础上，研究了一阶时滞微分方程的稳定性。证明了经典积分 Lyapunov-Zhukovskii 稳定性检验的类似物。与所有已知的相比，新的指数稳定性检验是在 Floquet 理论的基础上获得的。实现指数稳定性的可能性与解的振荡有关。