# A behavioral approach to data-driven control with noisy input-output data

arXiv: https://arxiv.org/abs/2206.08408 · HTML: https://mlsanity.com/paper/2206.08408/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2022.

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

- [Controller Synthesis from Noisy-Input Noisy-Output Data](https://mlsanity.com/paper/2402.02588/) (2024)
- [A New Perspective On AI Safety Through Control Theory Methodologies](https://mlsanity.com/paper/2506.23703/) (2025)

## Abstract (arXiv)

This paper deals with data-driven stability analysis and feedback stabillization of linear input-output systems in autoregressive (AR) form. We assume that noisy input-output data on a finite time-interval have been obtained from some unknown AR system. Data-based tests are then developed to analyse whether the unknown system is stable, or to verify whether a stabilizing dynamic feedback controller exists. If so, stabilizing controllers are computed using the data. In order to do this, we employ the behavioral approach to systems and control, meaning a departure from existing methods in data driven control. Our results heavily rely on a characterization of asymptotic stability of systems in AR form using the notion of quadratic difference form (QDF) as a natural framework for Lyapunov functions of autonomous AR systems. We introduce the concepts of informative data for quadratic stability and quadratic stabilization in the context of input-output AR systems and establish necessary and sufficient conditions for these properties to hold. In addition, this paper will build on results on quadratic matrix inequalties (QMIs) and a matrix version of Yakubovich's S-lemma.