# From noisy data to feedback controllers: non-conservative design via a matrix S-lemma

arXiv: https://arxiv.org/abs/2006.00870 · HTML: https://mlsanity.com/paper/2006.00870/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2020.

## Built on by (most cited first, 11 of 11)

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- [Stability-Certified On-Policy Data-Driven LQR via Recursive Learning and Policy Gradient](https://mlsanity.com/paper/2403.05367/) (2024)
- [End-to-end guarantees for indirect data-driven control of bilinear systems with finite stochastic data](https://mlsanity.com/paper/2409.18010/) (2024)
- [Data driven feedback linearization of nonlinear control systems via Lie derivatives and stacked regression approach](https://mlsanity.com/paper/2508.13241/) (2025)
- [Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems](https://mlsanity.com/paper/2504.08484/) (2025)
- [SAFE--MA--RRT: Multi-Agent Motion Planning with Data-Driven Safety Certificates](https://mlsanity.com/paper/2509.04413/) (2025)
- [Data-Driven Continuous-Time Linear Quadratic Regulator via Closed-Loop and Reinforcement Learning Parameterizations](https://mlsanity.com/paper/2604.27922/) (2026)
- [Model-Based and Data-Driven Hierarchical Control and Topology Co-Design for Robust Networked Systems](https://mlsanity.com/paper/2606.11596/) (2026)

## Abstract (arXiv)

We propose a new method to obtain feedback controllers of an unknown dynamical system directly from noisy input/state data. The key ingredient of our design is a new matrix S-lemma that will be proven in this paper. We provide both strict and non-strict versions of this S-lemma, that are of interest in their own right. Thereafter, we will apply these results to data-driven control. In particular, we will derive non-conservative design methods for quadratic stabilization, H_2 and H_inf control, all in terms of data-based linear matrix inequalities. In contrast to previous work, the dimensions of our decision variables are independent of the time horizon of the experiment. Our approach thus enables control design from large data sets.