AbstractDistributed algorithms for synchronization and consensus in multi‐agent networks are considered. The agents are assumed to be linear of arbitrary order, the interaction topology may switch, and the couplings are uncertain, assumed only to satisfy certain quadratic constraints. Using the Kalman‐Yakubovich‐Popov lemma and absolute stability theory techniques, consensus criteria for the networks of this type are obtained. These criteria extend a number of known results for agents with special dynamics and are close in spirit to the celebrated circle criterion for the stability of Lurie systems.