Robust Event-Based Control: Bridge Time-Domain Triggering and Frequency-Domain Uncertainties

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.