  While many event-triggered control strategies are available in the
literature, most of them are designed ignoring the presence of measurement
noise. As measurement noise is omnipresent in practice and can have detrimental
effects, for instance, by inducing Zeno behavior in the closed-loop system and
with that the lack of a positive lower bound on the inter-event times,
rendering the event-triggered control design practically useless, it is of
great importance to address this gap in the literature. To do so, we present a
general framework for set stabilization of (distributed) event-triggered
control systems affected by additive measurement noise. It is shown that, under
general conditions, Zeno-free static as well as dynamic triggering rules can be
designed such that the closed-loop system satisfies an input-to-state practical
set stability property. We ensure Zeno-freeness by proving the existence of a
uniform strictly positive lower-bound on the minimum inter-event time. The
general framework is applied to point stabilization and consensus problems as
particular cases, where we show that, under similar assumptions as the original
work, existing schemes can be redesigned to robustify them to measurement
noise. Consequently, using this framework, noise-robust triggering conditions
can be designed both from the ground up and by simple redesign of several
important existing schemes. Simulation results are provided that illustrate the
strengths of this novel approach.
