# Delta-operator based consensus analysis of multi-agent networks with link failures

## TL;DR

This paper introduces a delta-operator based framework for analyzing consensus in multi-agent networks with link failures, unifying discrete and continuous systems, and provides conditions for consensus and bounds on influence of faults.

## Contribution

It develops a delta-operator approach to unify discrete and continuous multi-agent systems and analyzes consensus under random link failures with quantification of fault influence.

## Key findings

- Consensus is achieved in mean, probability, and almost surely if the expected graph is strongly connected.
- The influence of faulty agents on the consensus value is quantified.
- Simulation confirms the theoretical results.

## Abstract

In this paper, a discrete-time multi-agent system is presented which is formulated in terms of the delta operator. The proposed multi-agent system can unify discrete-time and continuous-time multi-agent systems. In a multi-agent network, in practice, the communication among agents is acted upon by various factors. The communication network among faulty agents may cause link failures, which is modeled by randomly switching graphs. First, we show that the delta representation of discrete-time multi-agent system reaches consensus in mean (in probability and almost surely) if the expected graph is strongly connected. The results induce that the continuous-time multi-agent system with random networks can also reach consensus in the same sense. Second, the influence of faulty agents on consensus value is quantified under original network. By using matrix perturbation theory, the error bound is also presented in this paper. Finally, a simulation example is provided to demonstrate the effectiveness of our theoretical results.