Super-twisting over networks: A Lyapunov approach for distributed differentiation
Abstract
We study distributed differentiation, where agents in a networked system estimate the average of local time-varying signals and their derivatives under mild assumptions on the agents' signals and their first and second derivatives. Existing sliding-mode methods provide only local stability guarantees and lack systematic gain selection. By isolating the structural features shared with the super-twisting algorithm and encoding them into an abstract model, we construct a Lyapunov function enabling systematic gain design and proving global finite-time convergence to consensus for the distributed differentiator. Building on this framework, we develop an event-triggered hybrid system implementation using time-varying and state dependent threshold rules and derive minimum inter-event time guarantees and accuracy bounds that quantify the trade-off between estimation accuracy and communication effort.
Cite
@article{arxiv.2602.01857,
title = {Super-twisting over networks: A Lyapunov approach for distributed differentiation},
author = {Rodrigo Aldana-López and Irene Perez Salesa and David Gomez Gutierrez and Rosario Aragues and Carlos Sagues},
journal= {arXiv preprint arXiv:2602.01857},
year = {2026}
}
Comments
Preprint. Submitted for possible publication