# On infinitesimal contraction analysis for hybrid systems

arXiv: https://arxiv.org/abs/1811.03956 · HTML: https://mlsanity.com/paper/1811.03956/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Nov 2018.

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

- [Gait Switching and Enhanced Stabilization of Walking Robots with Deep Learning-based Reachability: A Case Study on Two-link Walker](https://mlsanity.com/paper/2409.16301/) (2024)

## Abstract (arXiv)

Infinitesimal contraction analysis, wherein global asymptotic convergence results are obtained from local dynamical properties, has proven to be a powerful tool for applications in biological, mechanical, and transportation systems. The technique has primarily been developed for systems governed by a single, possibly nonsmooth, differential or difference equation. We generalize infinitesimal contraction analysis to hybrid systems governed by interacting differential and difference equations. Importantly, we leverage an intrinsic distance function to derive the first contraction results for hybrid systems without restrictions on mode sequence or dwell time. Our theoretical results are illustrated in several examples and applications.