  This paper addresses the following question: "Suppose that a state-feedback
controller stabilizes an infinite-dimensional linear continuous-time system. If
we choose the parameters of an event/self-triggering mechanism appropriately,
is the event/self-triggered control system stable under all sufficiently small
nonlinear Lipschitz perturbations?" We assume that the stabilizing feedback
operator is compact. This assumption is used to guarantee the strict
positiveness of inter-event times and the existence of the mild solution of
evolution equations with unbounded control operators. First, for the case where
the control operator is bounded, we show that the answer to the above question
is positive, giving a sufficient condition for exponential stability, which can
be employed for the design of event/self-triggering mechanisms. Next, we
investigate the case where the control operator is unbounded and prove that the
answer is still positive for periodic event-triggering mechanisms.
