On Analytical Computation of Robustness Consensus for Unstable Multi‐Agent Systems Under Unknown Perturbations

ABSTRACT This article delves deeply into the robustness consensus problem in multi‐agent systems, which suffer from uncertainties under an undirected communication graph. We address the unstable and non‐minimum agents characterized as a general linear plant. To do this, a practical feedback protocol, that is, the filtered PID protocol, is exploited that aims to guarantee the consensus achievement for the system. This paper is dedicated to determining the utmost uncertainty variation so that the system continues to be consensusability using the same feedback protocols. Benefiting from a similar robust margin optimization technique, we derive the analytical expression of the intrinsic limit on the robustness consensus. Our results contribute to explaining how, in the context of certain uncertainties, the agent's unstable pole, non‐minimum phase zero, and the network connectivity in general curtail the robustness consensus margin that can be delivered. The results also reveal that by tuning the proper filter parameter, it is possible to raise the robustness consensus margin attainable.