Consensus between nonlinearly coupled discrete-time agents

The problem of consensus in discrete time multi-agent networks with nonlinear couplings is considered. The agents are identical but may have arbitrary order, the switching interaction topology and the couplings may be uncertain. We assume that the graph is undirected and remains connected, the couplings are anti-symmetric and satisfy some sector or, more generally, conic quadratic constraints. Using the Kalman-Szegö lemma and absolute stability theory techniques, consensus criteria for the networks of this type are obtained. These criteria are close in spirit to the celebrated Tsypkin and Jury-Lee criteria for stability of Lurie systems with sampled time.