On Topological Properties of the Set of Stabilizing Feedback Gains

• 成果类型: Article
• 署名作者: Bu, Jingjing; Mesbahi, Afshin; Mesbahi, Mehran
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2992510
• 发表日期: 2021
• 页码: 730-744
• 关键词: Control synthesis; feedback stabilization; topological and metrical analysis

摘要

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 inverted right perpendicularn 2inverted left perpendicular 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.