  This paper mainly investigates consensus problem with pull-based
event-triggered feedback control. For each agent, the diffusion coupling
feedbacks are based on the states of its in-neighbors at its latest triggering
time and the next triggering time of this agent is determined by its
in-neighbors' information as well. The general directed topologies, including
irreducible and reducible cases, are investigated. The scenario of distributed
continuous monitoring is considered firstly, namely each agent can observe its
in-neighbors' continuous states. It is proved that if the network topology has
a spanning tree, then the event-triggered coupling strategy can realize
consensus for the multi-agent system. Then the results are extended to
discontinuous monitoring, i.e., self-triggered control, where each agent
computes its next triggering time in advance without having to observe the
system's states continuously. The effectiveness of the theoretical results are
illustrated by a numerical example finally.
