# Further Geometric and Lyapunov Characterizations of Incrementally Stable Systems on Finsler Manifolds

arXiv: https://arxiv.org/abs/2002.11444 · HTML: https://mlsanity.com/paper/2002.11444/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2020.

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

- [KEEC: Koopman Embedded Equivariant Control](https://mlsanity.com/paper/2312.01544/) (2023)

## Abstract (arXiv)

In this paper, we report several new geometric and Lyapunov characterizations of incrementally stable systems on Finsler and Riemannian manifolds. A new and intrinsic proof of an important theorem in contraction analysis is given via the complete lift of the system. Based on this, two Lyapunov characterizations of incrementally stable systems are derived, namely, converse contraction theorems, and revelation of the connection between incremental stability and stability of an equilibrium point, in which the second result recovers and extends the classical Krasovskii's method.