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In this paper, we study the robustness of the event-triggered consensusalgorithms against frequency-domain uncertainties. It is revealed that thesampling errors resulted by event triggering are essentially images of linearfinite-gain $\mathcal{L}_2$-stable operators acting on the consensus errors ofthe sampled states and the event-triggered mechanism is equivalent to anegative feedback loop introduced additionally to the feedback system. Invirtue of this, the robust consensus problem of the event-triggered networksystems subject to additive dynamic uncertainties and network multiplicativeuncertainties are considered, respectively. In both cases, quantitativerelationships among the parameters of the controllers, the Laplacian matrix ofthe network topology, and the robustness against aperiodic event triggering andfrequency-domain uncertainties are unveiled. Furthermore, the event-triggereddynamic average consensus (DAC) problem is also investigated, wherein thesampling errors are shown to be images of nonlinear finite-gain operators. Therobust performance of the proposed DAC algorithm is analyzed, which indicatesthat the robustness and the performance are negatively related to theeigenratio of the Laplacian matrix. Simulation examples are also provided toverify the obtained results.

An Operator-Theoretic Approach to Robust Event-Triggered Control of Network Systems with Frequency-Domain Uncertainties