# Review on contraction analysis and computation of contraction metrics

arXiv: https://arxiv.org/abs/2203.01367 · HTML: https://mlsanity.com/paper/2203.01367/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2022.

## Built on by (most cited first, 1 of 1)

- [Neural Contraction Metrics with Formal Guarantees for Discrete-Time Nonlinear Dynamical Systems](https://mlsanity.com/paper/2504.17102/) (2025)

## Abstract (arXiv)

Contraction analysis considers the distance between two adjacent trajectories. If this distance is contracting, then trajectories have the same long-term behavior. The main advantage of this analysis is that it is independent of the solutions under consideration. Using an appropriate metric, with respect to which the distance is contracting, one can show convergence to a unique equilibrium or, if attraction only occurs in certain directions, to a periodic orbit. Contraction analysis was originally considered for ordinary differential equations, but has been extended to discrete-time systems, control systems, delay equations and many other types of systems. Moreover, similar techniques can be applied for the estimation of the dimension of attractors and for the estimation of different notions of entropy (including topological entropy). This review attempts to link the references in both the mathematical and the engineering literature and, furthermore, point out the recent developments and algorithms in the computation of contraction metrics.