# Convex Data-Driven Contraction With Riemannian Metrics

arXiv: https://arxiv.org/abs/2412.20283 · HTML: https://mlsanity.com/paper/2412.20283/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Dec 2024.

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

- [Frequency Response Identification of Low-Order Systems: Finite-Sample Analysis](https://mlsanity.com/paper/2508.17142/) (2025)
- [Delay Independent Safe Control with Neural Networks: Positive Lur'e Certificates for Risk Aware Autonomy](https://mlsanity.com/paper/2510.06661/) (2025)
- [Equation-Free Period-Aware Forecast-Error Contraction for Estimating Negative Largest Lyapunov Exponents from Short Trajectory Ensembles](https://mlsanity.com/paper/2608.05522/) (2026)

## Abstract (arXiv)

The growing complexity of dynamical systems and advances in data collection necessitates robust data-driven control strategies without explicit system identification and robust synthesis. Data-driven stability has been explored in linear and nonlinear systems, often by turning the problem into a linear or positive semidefinite program. This paper focuses on a new emerging property called contractivity, which refers to the exponential convergence of all system trajectories toward each other under a specified metric. Data-driven closed loop contractivity has been studied for the case of the 2-norm and assuming nonlinearities are Lipschitz bounded in subsets of n dimensional euclidean space. We extend the analysis by considering Riemannian metrics for polynomial dynamics. The key to our derivation is to leverage the convex criteria for closed-loop contraction and duality results to efficiently check infinite dimensional membership constraints. Numerical examples demonstrate the effectiveness of the proposed method for both linear and nonlinear systems, highlighting its potential for robust data-driven contraction.