We propose a geometric method to determine the stability region of the zero solution of a linear periodic difference equation via the delayed feedback control (briefly, DFC) with the commuting feedback gain. For the equation, our method is more effective than the Jury criterion. First, we give a relationship, named the C-map theorem, between the characteristic multipliers of an original equation and those of the equation via DFC. Next, we show the existence and m-starlike property, defined in this paper, of an m-closed curve induced from the C-map. Using this result, we prove that the region enclosed by the m-closed curve is the stability region of the zero solution of the equation via DFC.

我们提出了一种几何方法，通过具有换向反馈增益的延迟反馈控制（简称DFC）来确定线性周期差分方程零解的稳定区域。对于方程，我们的方法比陪审团标准更有效。首先，我们给出了原始方程的特征乘数与通过 DFC 得到的方程的特征乘数之间的关系，称为C-map 定理。接下来，我们展示了从 C 图导出的m 闭合曲线的存在性和m星状性质（在本文中定义） 。利用这个结果，我们通过 DFC 证明了m闭曲线所包围的区域是方程零解的稳定区域。