Synchronization of networks of piecewise-smooth systems

TL;DR

This paper investigates synchronization in networks of piecewise-smooth systems, introducing a novel discontinuous coupling method to ensure global synchronizability, supported by theoretical generalizations and extensive numerical simulations.

Contribution

It generalizes QUAD system results to PWS systems and proposes a discontinuous coupling approach for guaranteed global synchronization.

Findings

Discontinuous coupling guarantees global synchronizability.

Generalization of QUAD results to PWS systems.

Numerical simulations validate the approach.

Abstract

We study convergence in networks of piecewise-smooth (PWS) systems that commonly arise in applications to model dynamical systems whose evolution is affected by macroscopic events such as switches and impacts. Existing approaches were typically oriented toward guaranteeing global bounded synchronizability, local stability of the synchronization manifold, or achieving synchronization by exerting a control action on each node. Here we start by generalizing existing results on QUAD systems to the case of PWS systems, accounting for a large variety of nonlinear coupling laws. Then, we propose that a discontinuous coupling can be used to guarantee global synchronizability of a network of N PWS agents under mild assumptions on the individual dynamics. We provide extensive numerical simulations to gain insights on larger networks.