Event-Based Robust Stabilization: An Operator-Theoretic Approach

This paper considers the robustness of event-triggered control of general linear systems against additive frequency-domain uncertainties. It is revealed that in the event-triggered mechanisms, the sampling errors are images of affine operators acting on the sampled outputs. Though not belonging to $\mathcal{R}{\mathcal{H}_\infty }$, these operators are finite-gain ℒ
2
stable with operator-norm depending on the triggering conditions and the norm bound of the uncertainties. Moreover, the robust event-triggered controller design problem can then be transformed into a standard H
∞
synthesis problem of a linear system having the same order as the controlled plant. Algorithms are also provided to construct the event-triggered robust dynamic output-feedback controllers.