On Non-Consensus Motions of Dynamical Linear Multi-Agent Systems

TL;DR

This paper investigates why high-order linear multi-agent systems fail to reach consensus, classifies various non-consensus behaviors based on system parameters, and supports findings with numerical examples.

Contribution

It provides a comprehensive classification of non-consensus motions in high-order linear multi-agent systems based on dynamics, protocols, and topology.

Findings

Identifies conditions leading to non-consensus behaviors

Classifies different types of non-consensus phases

Validates analysis with numerical simulations

Abstract

The non-consensus problems of high order linear time-invariant dynamical homogeneous multi-agent systems are concerned. Based on the conditions of consensus achievement, the mechanisms that lead to non-consensus motions are analyzed. Besides, a comprehensive classification for diverse types of non-consensus phases in accordance to the different conditions is conducted, which is jointly depending on the self-dynamics of agents, the interactive protocol and the graph topology. A series of numerical examples are demonstrated to illustrate the theoretical analysis.