Nonlinear consensus protocols with applications to quantized systems

TL;DR

This paper studies nonlinear consensus protocols with nonlinear measurements and communication, proving their stability on directed and undirected graphs, and extends results to quantized systems, broadening applicability.

Contribution

It introduces a unified analysis of nonlinear consensus protocols using Filippov solutions and extends quantized consensus results to directed graphs.

Findings

Proves asymptotic stability of nonlinear consensus systems.

Extends quantized consensus results from undirected to directed graphs.

Handles discontinuities via Filippov solutions.

Abstract

Two types of general nonlinear consensus protocols are considered in this paper, namely the systems with nonlinear measurement and communication of the agents' states, respectively. The solutions of the systems are understood in the sense of Filippov to handle the possible discontinuity of the nonlinear functions. For each case, we prove the asymptotic stability of the systems defined on both directed and undirected graphs. Then we reinterpret the results about the general models for a specific type of systems, i.e., the quantized consensus protocols, which extend some existing results (e.g., [1,2]) from undirected graphs to directed ones.