Super-twisting over networks: A Lyapunov approach for distributed differentiation
Rodrigo Aldana‐López, Irene Perez-Salesa, David Gómez‐Gutiérrez, Rosario Aragüés, Carlos Sagüés · Nonlinear Analysis Hybrid Systems · 2026
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 that enables systematic gain design and proves global finite-time convergence to consensus for the distributed differentiator. Building on this framework, we develop an event-triggered 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 for the networked system.