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

arXiv: https://arxiv.org/abs/1904.02737 · HTML: https://mlsanity.com/paper/1904.02737/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2019.

## Built on by (most cited first, 7 of 7)

- [Robot Fleet Learning via Policy Merging](https://mlsanity.com/paper/2310.01362/) (2023)
- [Global Convergence of Direct Policy Search for State-Feedback H_∞ Robust Control: A Revisit of Nonsmooth Synthesis with Goldstein Subdifferential](https://mlsanity.com/paper/2210.11577/) (2022)
- [Towards a Theoretical Foundation of Policy Optimization for Learning Control Policies](https://mlsanity.com/paper/2210.04810/) (2022)
- [Asynchronous Distributed Reinforcement Learning for LQR Control via Zeroth-Order Block Coordinate Descent](https://mlsanity.com/paper/2107.12416/) (2021)
- [Optimization Landscape of Policy Gradient Methods for Discrete-time Static Output Feedback](https://mlsanity.com/paper/2310.19022/) (2023)
- [On the Optimization Landscape of Dynamic Output Feedback: A Case Study for Linear Quadratic Regulator](https://mlsanity.com/paper/2209.05042/) (2022)
- [Bridging Continuous-time LQR and Reinforcement Learning via Gradient Flow of the Bellman Error](https://mlsanity.com/paper/2506.09685/) (2025)

## 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.