On the stability and convergence of a class of consensus systems with a nonlinear input

TL;DR

This paper analyzes the stability and convergence of nonlinear input-driven consensus systems, providing conditions for their stability and illustrating with a real-world IoT application example.

Contribution

It introduces conditions for convergence and stability of a class of nonlinear consensus systems and offers a rigorous proof of these properties.

Findings

Conditions for convergence and stability are derived.

The system converges to a Lur'e-like scalar system under certain conditions.

An example application in a speed advisory IoT system is provided.

Abstract

We consider a class of consensus systems driven by a nonlinear input. Such systems arise in a class of IoT applications. Our objective in this paper is to determine conditions under which a certain partially distributed system converges to a Lur'e-like scalar system, and to provide a rigorous proof of its stability. Conditions are derived for the non-uniform convergence and stability of such a system and an example is given of a speed advisory system where such a system arises in real engineering practice.