# Connectivity of the Feasible and Sublevel Sets of Dynamic Output Feedback Control with Robustness Constraints

arXiv: https://arxiv.org/abs/2203.11177 · HTML: https://mlsanity.com/paper/2203.11177/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2022.

## Built on by (most cited first, 6 of 6)

- [Learning the Kalman Filter with Fine-Grained Sample Complexity](https://mlsanity.com/paper/2301.12624/) (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)
- [Model-Free μ-Synthesis: A Nonsmooth Optimization Perspective](https://mlsanity.com/paper/2402.11654/) (2024)
- [On the Optimization Landscape of Observer-based Dynamic Linear Quadratic Control](https://mlsanity.com/paper/2604.10635/) (2026)
- [Algorithmic Optimality Guarantees for Nonsmooth H_∞ Output-Feedback Policy Search](https://mlsanity.com/paper/2609.06197/) (2026)

## Abstract (arXiv)

This paper considers the optimization landscape of linear dynamic output feedback control with H_∞ robustness constraints. We consider the feasible set of all the stabilizing full-order dynamical controllers that satisfy an additional H_∞ robustness constraint. We show that this H_∞-constrained set has at most two path-connected components that are diffeomorphic under a mapping defined by a similarity transformation. Our proof technique utilizes a classical change of variables in H_∞ control to establish a subjective mapping from a set with a convex projection to the H_∞-constrained set. This proof idea can also be used to establish the same topological properties of strict sublevel sets of linear quadratic Gaussian (LQG) control and optimal H_∞ control. Our results bring positive news for gradient-based policy search on robust control problems.