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On Topological and Metrical Properties of Stabilizing Feedback Gains: the MIMO Case

arXiv 1904.02737 ↗First posted 4 Apr 2019eess.SY cs.SYcited by 6

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Abstract (arXiv)

In this paper, we discuss various topological and metrical aspects of the set of stabilizing static feedback gains for multiple-input-multiple-output (MIMO) linear-time-invariant (LTI) systems, in both continuous and discrete-time. Recently, connectivity properties of this set (for continuous time) have been reported in the literature, along with a discussion on how this connectivity is affected by restricting the feedback gain to linear subspaces. We show that analogous to the continuous-time case, one can construct instances where the set of stabilizing feedback gains for discrete time LTI systems has exponentially many connected components.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). First posted on arXiv 4 Apr 2019.

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Citing papers per year: 2021: 1; 2022: 3; 2023: 2.

6 papers.

  1. 2023Robot Fleet Learning via Policy Mergingcited by 11
  2. 2022Towards a Theoretical Foundation of Policy Optimization for Learning Control Policiescited by 6
  3. 2022Global Convergence of Direct Policy Search for State-Feedback H_∞ Robust Control: A Revisit of Nonsmooth Synthesis with Goldstein Subdifferentialcited by 6
  4. 2021Asynchronous Distributed Reinforcement Learning for LQR Control via Zeroth-Order Block Coordinate Descentcited by 4
  5. 2023Optimization Landscape of Policy Gradient Methods for Discrete-time Static Output Feedbackcited by 2
  6. 2022On the Optimization Landscape of Dynamic Output Feedback: A Case Study for Linear Quadratic Regulatorcited by 1