Abstract A general theorem is proved on the stability of an equilibrium point of a nonlinear delay differential equation, in the critical case when zero is a simple root of the characteristic equation for linearized equation. It extends the classical theorem of Malkin from the case of ordinary differential equations. An application to the case of a electrohydraulic governor with delay in control is given.

中文翻译：

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时滞微分方程平衡稳定性的一个临界案例及电液伺服机构模型的研究

摘要 证明了非线性时滞微分方程平衡点稳定性的一般定理，在零为线性化方程特征方程单根的临界情况下。它从常微分方程的情况扩展了马尔金的经典定理。给出了具有控制延迟的电液调速器的应用。