Abstract We consider the stability region of monic polynomials in the coefficient space. Starting from specially chosen stable points we define polytopes, whose edges are either stable or belong to the stability boundary. Therefore by the Edge Theorem the interiors are stable. Stable polytopes, in the reverse directions which are directed to infinity have been studied in the work (Dzhafarov et al., 2019). Some applications of the obtained results to the synthesis of fixed-order stabilizing controllers are given.

中文翻译：

---

赫尔维茨地区的多胞体

摘要 我们考虑了系数空间中一元多项式的稳定域。从特别选择的稳定点开始，我们定义多面体，其边缘要么是稳定的，要么属于稳定边界。因此根据边缘定理，内部是稳定的。在工作中研究了指向无穷大的相反方向的稳定多胞体（Dzhafarov 等人，2019 年）。给出了所得结果在定阶稳定控制器合成中的一些应用。