  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.
