# Consensus and Flocking under Communication Failures for a Class of Cucker-Smale Systems

## TL;DR

This paper establishes conditions under which multi-agent systems modeled by generalized Cucker-Smale dynamics achieve consensus and flocking despite communication failures, using Lyapunov methods and connectivity persistence.

## Contribution

It introduces a novel approach combining Lyapunov design with a persistence condition based on algebraic connectivity to analyze flocking under communication failures.

## Key findings

- Derived sufficient conditions for consensus and flocking.
- Provided quantitative decay estimates for system variance.
- Linked algebraic connectivity to system robustness against failures.

## Abstract

In this paper, we study sufficient conditions for the emergence of asymptotic consensus and flocking in a certain class of non-linear generalised Cucker-Smale systems subject to multiplicative communication failures. Our approach is based on the combination of strict Lyapunov design together with the formulation of a suitable persistence condition for multi-agent systems. The latter can be interpreted as a lower bound on the algebraic connectivity of the time-average of the interaction graph generated by the communication weights, and provides quantitative decay estimates for the variance functional along the solutions of the system.