  This paper examines the event-triggered consensus of the multi-agent system
on matrix-weighted networks, where the interdependencies among
higher-dimensional states of neighboring agents are characterized by
matrix-weighted edges in the network. Specifically, a novel distributed dynamic
event-triggered coordination strategy is proposed for this category of
generalized networks, in which an auxiliary system is employed for each agent
to dynamically adjust the triggering threshold, which plays an essential role
in guaranteeing that the triggering time sequence does not exhibit Zeno
behavior. Distributed event-triggered control protocols are proposed to
guarantee leaderless and leader-follower consensus for multi-agent systems on
matrix-weighted networks, respectively. Remarkably, the spectrum of
matrix-valued weights is crucial in event-triggered mechanism design for
matrix-weighted networks, generalizing those results only applicable for
scalar-weighted networks. The proposed approach allows each agent to broadcast
and receive information only at its triggering instants. Finally, simulation
examples are provided to demonstrate the theoretical results.
