Event-triggered consensus of multi-agent systems under directed topology based on periodic sampled-data

TL;DR

This paper addresses event-triggered consensus in multi-agent systems with directed graphs, allowing large sampling periods and finite delays, using a novel positive series method for convergence analysis.

Contribution

It introduces a new consensus algorithm for directed multi-agent systems with periodic sampling, accommodating large sampling periods and bounded delays, extending to general topologies.

Findings

Consensus achieved under large sampling periods

Finite delays are manageable if bounded by sampling period

Effective convergence analysis via positive series method

Abstract

The event-triggered consensus problem of first-order multi-agent systems under directed topology is investigated. The event judgements are only implemented at periodic time instants. Under the designed consensus algorithm, the sampling period is permitted to be arbitrarily large. Another advantage of the designed consensus algorithm is that, for systems with time delay, consensus can be achieved for any finite delay only if it is bounded by the sampling period. The case of strongly connected topology is first investigated. Then, the result is extended to the most general topology which only needs to contain a spanning tree. A novel method based on positive series is introduced to analyze the convergence of the closed-loop systems. A numerical example is provided to illustrate the effectiveness of the obtained theoretical results.