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

TL;DR

This paper presents an operator-theoretic framework for analyzing the robustness of event-triggered consensus algorithms in network systems with frequency-domain uncertainties, revealing key relationships between system parameters and robustness.

Contribution

It introduces a novel operator-based approach to quantify robustness of event-triggered control under frequency uncertainties, including dynamic average consensus.

Findings

Sampling errors are images of linear finite-gain operators.

Robustness depends on controller parameters, network topology, and eigenratio of the Laplacian.

Simulation verifies the theoretical robustness and performance relationships.

Abstract

In this paper, we study the robustness of the event-triggered consensus algorithms against frequency-domain uncertainties. It is revealed that the sampling errors resulted by event triggering are essentially images of linear finite-gain $\mathcal{L}_2$-stable operators acting on the consensus errors of the sampled states and the event-triggered mechanism is equivalent to a negative feedback loop introduced additionally to the feedback system. In virtue of this, the robust consensus problem of the event-triggered network systems subject to additive dynamic uncertainties and network multiplicative uncertainties are considered, respectively. In both cases, quantitative relationships among the parameters of the controllers, the Laplacian matrix of the network topology, and the robustness against aperiodic event triggering and frequency-domain uncertainties are unveiled. Furthermore, the event-triggered dynamic average consensus (DAC) problem is also investigated, wherein the sampling errors are shown to be images of nonlinear finite-gain operators. The robust performance of the proposed DAC algorithm is analyzed, which indicates that the robustness and the performance are negatively related to the eigenratio of the Laplacian matrix. Simulation examples are also provided to verify the obtained results.