This article presents a fairly complete account on various topological and metrical aspects of feedback stabilization for single-input single-output (SISO) continuous and discrete time linear time-invariant (LTI) systems. In particular, we prove that the set of stabilizing output feedback gains for a SISO system with n states have at most [n/2] connected components. Furthermore, our analysis yields an algorithm for determining intervals of stabilizing gains for general continuous and discrete LTI systems; the proposed algorithm also computes the number of unstable roots in each unstable interval.

中文翻译：

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稳定反馈增益集的拓扑性质


本文对单输入单输出 (SISO) 连续和离散时间线性时不变 (LTI) 系统的反馈稳定的各个拓扑和度量方面进行了相当完整的说明。特别是，我们证明了具有 n 个状态的 SISO 系统的稳定输出反馈增益集最多具有 [n/2] 个连接组件。此外，我们的分析产生了一种算法，用于确定一般连续和离散 LTI 系统的稳定增益区间；该算法还计算每个不稳定区间中不稳定根的数量。