  This paper considers the robustness of event-triggered control of general
linear systems against additive or multiplicative frequency-domain
uncertainties. It is revealed that in static or dynamic event triggering
mechanisms, the sampling errors are images of affine operators acting on the
sampled outputs. Though not belonging to $\mathcal{RH}_\infty$, these operators
are finite-gain $\mathcal{L}_2$ stable with operator-norm depending on the
triggering conditions and the norm bound of the uncertainties. This
characterization is further extended to the general integral quadratic
constraint (IQC)-based triggering mechanism. As long as the triggering
condition characterizes an $\mathcal{L}_2$-to-$\mathcal{L}_2$ mapping
relationship (in other words, small-gain-type constraints) between the sampled
outputs and the sampling errors, the robust event-triggered controller design
problem can be transformed into the standard $H_\infty$ synthesis problem of a
linear system having the same order as the controlled plant. Algorithms are
provided to construct the robust controllers for the static, dynamic and
IQC-based event triggering cases.
