# Guaranteed Stability Margins for Decentralized Linear Quadratic Regulators

arXiv: https://arxiv.org/abs/2304.07576 · HTML: https://mlsanity.com/paper/2304.07576/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Apr 2023.

## Built on by (most cited first, 1 of 1)

- [Exploiting inter-agent coupling information for efficient reinforcement learning of cooperative LQR](https://mlsanity.com/paper/2504.20927/) (2025)

## Abstract (arXiv)

It is well-known that linear quadratic regulators (LQR) enjoy guaranteed stability margins, whereas linear quadratic Gaussian regulators (LQG) do not. In this letter, we consider systems and compensators defined over directed acyclic graphs. In particular, there are multiple decision-makers, each with access to a different part of the global state. In this setting, the optimal LQR compensator is dynamic, similar to classical LQG. We show that when sub-controller input costs are decoupled (but there is possible coupling between sub-controller state costs), the decentralized LQR compensator enjoys similar guaranteed stability margins to classical LQR. However, these guarantees disappear when cost coupling is introduced.