Consensus in discrete-time nonlinearly coupled networks

We consider consensus algorithms for multi-agent networks with discrete-time linear identical MIMO agents. The agents may be of arbitrary order, the interaction topology may be time-varying and the couplings may be nonlinear and uncertain, however assumed to satisfy a slope restriction or, more generally, quadratic constraint. Using the discrete-time version of the KYP Lemma (referred to as the Kalman-Szeg¨o Lemma), we derive a criterion which provide consensus in such a network for any uncertain couplings from the mentioned class. This criterion is close in spirit to the celebrated Tsypkin criterion for discrete time Lurie system