  In this paper, we study consensus problem in multi-agent system with directed
topology by event-triggered feedback control. That is, at each agent, the
diffusion coupling feedbacks are based on the information from its latest
observations to its in-neighbours. We derive distributed criteria to determine
the next observation time of each agent that are triggered by its
in-neighbours' information and its own states respectively. We prove that if
the network topology is irreducible, then under the event-triggered coupling
principles, the multi-agent system reach consensus. Then, we extend these
results to the case of reducible topology with spanning tree. In addition,
these results are also extended to the case of self-triggered control, in terms
that the next triggering time of each agent is computed based on the current
states, i.e., without observing the system's states continuously. The
effectiveness of the theoretical results are illustrated by numerical examples.
