Edges' Riemannian energy analysis for synchronization of multi-agent nonlinear systems over undirected weighted graphs

TL;DR

This paper introduces a Riemannian energy-based method for ensuring global exponential synchronization in multi-agent nonlinear systems over undirected graphs, providing new conditions for distributed control design.

Contribution

It develops a novel Riemannian metric approach and Lyapunov function construction for analyzing and guaranteeing synchronization without leader nodes.

Findings

Established sufficient conditions for synchronization

Designed a distributed state-feedback control law

Proved global exponential convergence of the network

Abstract

In this note we investigate the problem of global exponential synchronization of multi-agent systems described by nonlinear input affine dynamics. We consider the case of networks described by undirected connected graphs possibly without leader. We present a set of sufficient conditions based on a Riemannian metric approach in order to design a state-feedback distributed control law. Then, we study the convergence properties of the overall network. By exploiting the properties of the edge Laplacian we construct a Lyapunov function that allows to conclude global exponential synchronization of the overall network.