Super-twisting over networks: A Lyapunov approach for distributed differentiation

TL;DR

This paper introduces a Lyapunov-based approach for distributed differentiation over networks, achieving global finite-time convergence and systematic gain design, with an event-triggered implementation balancing accuracy and communication.

Contribution

It develops a Lyapunov framework for distributed super-twisting algorithms, enabling systematic gain selection and global convergence guarantees.

Findings

Achieves global finite-time convergence to consensus.

Provides systematic gain design methodology.

Develops an event-triggered implementation with communication efficiency.

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.