Consensus analysis of large-scale nonlinear homogeneous multi-agent   formations with polynomial dynamics
  Drawing inspiration from the theory of linear "decomposable systems", we provide a method, based on linear matrix inequalities (LMIs), which makes it possible to prove the convergence (or consensus) of a set of interacting agents with polynomial dynamic. We also show that the use of a generalised version of the famous Kalman-Yakubovic-Popov lemma allows the development of an LMI test whose size does not depend on the number of agents. The method is validated experimentally on two academic examples. 
Paolo Massioni and G\'erard Scorletti
cs.SY