# On Topological Properties of the Set of Stabilizing Feedback Gains

arXiv: https://arxiv.org/abs/1904.08451 · HTML: https://mlsanity.com/paper/1904.08451/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Apr 2019.

## Built on by (most cited first, 5 of 5)

- [Model-Free Learning for the Linear Quadratic Regulator over Rate-Limited Channels](https://mlsanity.com/paper/2401.01258/) (2024)
- [Stability-Certified On-Policy Data-Driven LQR via Recursive Learning and Policy Gradient](https://mlsanity.com/paper/2403.05367/) (2024)
- [Policy Gradient Method for LQG Control via Input-Output-History Representation: Convergence to O(ε)-Stationary Points](https://mlsanity.com/paper/2510.19141/) (2025)
- [Model-Free Output Feedback Stabilization via Policy Gradient Methods](https://mlsanity.com/paper/2601.19284/) (2026)
- [On the Optimization Landscape of Observer-based Dynamic Linear Quadratic Control](https://mlsanity.com/paper/2604.10635/) (2026)

## Abstract (arXiv)

This work 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 has at most lceilfracn2rceil connected components. Furthermore, our analysis yields an algorithm for determining intervals of stabilizing gains for general continuous and discrete LIT systems; the proposed algorithm also computes the number of unstable roots in each unstable interval. Along the way, we also make a number of observations on the set of stabilizing state feedback gains for MIMO systems.