# Controller Synthesis from Noisy-Input Noisy-Output Data

arXiv: https://arxiv.org/abs/2402.02588 · HTML: https://mlsanity.com/paper/2402.02588/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 4 Feb 2024.

## Builds on (most cited first, 14 of 14)

- [Formulas for Data-driven Control: Stabilization, Optimality and Robustness](https://mlsanity.com/paper/1903.06842/) (2019)
- [Data-Enabled Predictive Control: In the Shallows of the DeePC](https://mlsanity.com/paper/1811.05890/) (2018)
- [Combining Prior Knowledge and Data for Robust Controller Design](https://mlsanity.com/paper/2009.05253/) (2020)
- [Provably robust verification of dissipativity properties from data](https://mlsanity.com/paper/2006.05974/) (2020)
- [Data-driven control via Petersen's lemma](https://mlsanity.com/paper/2109.12175/) (2021)
- [On a Stochastic Fundamental Lemma and Its Use for Data-Driven Optimal Control](https://mlsanity.com/paper/2111.13636/) (2021)
- [Quadratic matrix inequalities with applications to data-based control](https://mlsanity.com/paper/2203.12959/) (2022)
- [A behavioral approach to data-driven control with noisy input-output data](https://mlsanity.com/paper/2206.08408/) (2022)
- [Notes on data-driven output-feedback control of linear MIMO systems](https://mlsanity.com/paper/2311.17484/) (2023)
- [On data-driven control: informativity of noisy input-output data with cross-covariance bounds](https://mlsanity.com/paper/2111.14193/) (2021)
- [Data-driven Output-feedback Predictive Control: Unknown Plant's Order and Measurement Noise](https://mlsanity.com/paper/2201.03136/) (2022)
- [Data-Driven Stabilizing and Robust Control of Discrete-Time Linear Systems with Error in Variables](https://mlsanity.com/paper/2210.13430/) (2022)
- [Superstabilizing Control of Discrete-Time ARX Models under Error in Variables](https://mlsanity.com/paper/2210.14893/) (2022)
- [Model-based and Data-based Dynamic Output Feedback for Externally Positive Systems](https://mlsanity.com/paper/2305.02472/) (2023)

## Built on by (most cited first, 2 of 2)

- [Interpolation Conditions for Data Consistency and Prediction in Noisy Linear Systems](https://mlsanity.com/paper/2504.08484/) (2025)
- [Learning Neural Feedback Linearization for Data-driven Systems via Augmented Lagrangian](https://mlsanity.com/paper/2609.25163/) (2026)

## Abstract (arXiv)

We consider the problem of synthesizing a dynamic output-feedback controller for a linear system, using solely input-output data corrupted by measurement noise. To handle input-output data, an auxiliary representation of the original system is introduced. By exploiting the structure of the auxiliary system, we design a controller that robustly stabilizes all possible systems consistent with data. Notably, we also provide a novel solution to extend the results to generic multi-input multi-output systems. The findings are illustrated by numerical examples.