  This paper studies the consensus control problem faced with three essential
demands, namely, discrete control updating for each agent, discrete-time
communications among neighboring agents, and the fully distributed fashion of
the controller implementation without requiring any global information of the
whole network topology. Noting that the existing related results only meeting
one or two demands at most are essentially not applicable, in this paper we
establish a novel framework to solve the problem of fully distributed consensus
with discrete communication and control. The first key point in this framework
is the design of controllers that are only updated at discrete event instants
and do not depend on global information by introducing time-varying gains
inspired by the adaptive control technique. Another key point is the invention
of novel dynamic triggering functions that are independent of relative
information among neighboring agents. Under the established framework, we
propose fully distributed state-feedback event-triggered protocols for
undirected graphs and also further study the more complexed cases of
output-feedback control and directed graphs. Finally, numerical examples are
provided to verify the effectiveness of the proposed event-triggered protocols.
