Consensus of A Class of Nonlinear Systems with Varying Topology: A Hilbert Metric Approach

TL;DR

This paper presents a new Hilbert metric-based method for analyzing consensus in nonlinear systems with changing network topologies, offering more flexible and stronger results than existing approaches.

Contribution

It introduces a novel Hilbert metric approach that relaxes assumptions and simplifies proofs for nonlinear consensus with varying topology.

Findings

Provides a flexible framework for nonlinear consensus analysis.

Relaxes technical assumptions compared to standard methods.

Yields stronger conclusions with shorter proofs.

Abstract

In this technical note, we introduce a novel approach to studying consensus of continuous-time nonlinear systems with varying topology based on Hilbert metric. We demonstrate that this metric offers significant flexibility in analyzing consensus properties, while effectively handling nonlinearities and time dependencies. Notably, our approach relaxes key technical assumptions from some standard results while yielding stronger conclusions with shorter proofs. This framework provides new insights into nonlinear consensus under varying topology.