ABSTRACT We consider an automatic control system with a three-position relay of hysteresis type and a continuous periodic external disturbance. The purpose of the paper is to define the values of the system parameters at which periodic modes exist. A theorem on the existence of periodic solutions is proved. We provide an application with a numerical example to support the theorem.

中文翻译：

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三位置继电器自动控制系统中周期性模态的存在

摘要 我们考虑一个具有迟滞型三位继电器和连续周期性外部干扰的自动控制系统。本文的目的是定义存在周期性模式的系统参数值。证明了一个关于周期解存在性的定理。我们提供了一个带有数值示例的应用程序来支持该定理。