  This paper addresses the problem of event-triggered control for
infinite-dimensional systems. We employ event-triggering mechanisms that
compare the plant state and the error of the control input induced by the
event-triggered implementation. Under the assumption that feedback operators
are compact, a strictly positive lower bound on the inter-event times can be
guaranteed. We show that if the threshold of the event-triggering mechanisms is
sufficiently small, then the event-triggered control system with a bounded
control operator and a compact feedback operator is exponentially stable. For
infinite-dimensional systems with unbounded control operators, we employ two
event-triggering mechanisms that are based on system decomposition and periodic
event-triggering, respectively, and then analyze the exponential stability of
the closed-loop system under each event-triggering mechanism.
