  This paper studies the consensus problem of multi-agent systems with
asymmetric and reducible topologies. Centralized event-triggered rules are
provided so as to reduce the frequency of system's updating. The diffusion
coupling feedbacks of each agent are based on the latest observations from its
in-neighbors and the system's next observation time is triggered by a criterion
based on all agents' information. The scenario of continuous monitoring is
first considered, namely all agents' instantaneous states can be observed. It
is proved that if the network topology has a spanning tree, then the
centralized event-triggered coupling strategy can realize consensus for the
multi-agent system. Then the results are extended to discontinuous monitoring,
where the system computes its next triggering time in advance without having to
observe all agents' states continuously. Examples with numerical simulation are
provided to show the effectiveness of the theoretical results.
