Consensus Between Nonlinearly Coupled Agents with Heterogeneous Input Delays: Analytic Criteria

The paper addresses the problem of consensus robustness against small heterogeneous input delays in the agents. The agents are assumed to have first-order dynamics and may be nonlinearly coupled; the couplings maps may be uncertain, assumed only to satisfy a sector (slope) restriction and a symmetry condition. The topology of the network may be switching and uncertain, however, it is supposed to be undirected and uniformly connected (which is known to be almost necessary for consensus). Under the mentioned assumptions, we obtain explicit analytical conditions for the consensus robustness.