It is shown that the classic Nyquist criterion can be extended in a straightforward way to feedback systems of fractional order. The proof of this extension merely requires basic notions of vector analysis and of closed-loop system transfer functions. The criterion can be used not only to ascertain the stability of a fractional-order system but also to detect the presence of closed-loop poles inside any given sector of the complex plane. The test is finally applied to three examples of didactic value.

中文翻译：

---

分数阶反馈系统的奈奎斯特准则的初阶推导

结果表明，经典的奈奎斯特准则可以直接扩展到分数阶反馈系统。这种扩展的证明仅需要矢量分析和闭环系统传递函数的基本概念。该标准不仅可以用于确定分数阶系统的稳定性，而且可以用于检测复平面任何给定扇区内是否存在闭环极点。该测试最终应用于教学价值的三个示例。