# A Matrix Finsler's Lemma with Applications to Data-Driven Control

arXiv: https://arxiv.org/abs/2103.13461 · HTML: https://mlsanity.com/paper/2103.13461/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2021.

## Built on by (most cited first, 3 of 3)

- [LMI-based Data-Driven Robust Model Predictive Control](https://mlsanity.com/paper/2303.04777/) (2023)
- [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)

In a recent paper it was shown how a matrix S-lemma can be applied to construct controllers from noisy data. The current paper complements these results by proving a matrix version of the classical Finsler's lemma. This matrix Finsler's lemma provides a tractable condition under which all matrix solutions to a quadratic equality also satisfy a quadratic inequality. We will apply this result to bridge known data-driven control design techniques for both exact and noisy data, thereby revealing a more general theory. The result is also applied to data-driven control of Lur'e systems.