Master stability function for piecewise smooth networks

TL;DR

This paper extends the Master Stability Function framework to analyze synchronization in networks of identical piecewise smooth systems, providing explicit solutions and stability criteria for non-smooth dynamics.

Contribution

It introduces a novel extension of the Master Stability Function to piecewise smooth networks, enabling stability analysis of non-smooth synchronized systems.

Findings

Explicit characterization of the fundamental matrix solution

Extension of MSF to non-smooth dynamics

Framework for analyzing synchronization stability

Abstract

We consider a network of identical piecewise smooth systems that synchronizes on the manifold given by a periodic orbit of a single agent. We explicitly characterize the fundamental matrix solution of the network along the synchronous solution and extend the Master Stability Function tool to the present case of non-smooth dynamics.