# On the existence of KKL observers with nonlinear contracting dynamics (Long Version)

arXiv: https://arxiv.org/abs/2402.16432 · HTML: https://mlsanity.com/paper/2402.16432/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2024.

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

- [KKL Observer Synthesis for Nonlinear Systems via Physics-Informed Learning](https://mlsanity.com/paper/2501.11655/) (2025)
- [Verifiable Error Bounds for Physics-Informed Neural KKL Observers](https://mlsanity.com/paper/2603.20434/) (2026)
- [A KKL Observer Perspective on Reservoir Computing](https://mlsanity.com/paper/2610.04343/) (2026)

## Abstract (arXiv)

KKL (Kazantzis-Kravaris/Luenberger) observers are based on the idea of immersing a given nonlinear system into a target system that is a linear stable filter of the measured output. In the present paper, we extend this theory by allowing this target system to be a nonlinear contracting filter of the output. We prove, under a differential observability condition, the existence of these new KKL observers. We motivate their introduction by showing numerically the possibility of combining convergence speed and robustness to noise, unlike what is known for linear filtering.