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Drawing inspiration from the theory of linear "decomposable systems", weprovide a method, based on linear matrix inequalities (LMIs), which makes itpossible to prove the convergence (or consensus) of a set of interacting agentswith polynomial dynamic. We also show that the use of a generalised version ofthe famous Kalman-Yakubovic-Popov lemma allows the development of an LMI testwhose size does not depend on the number of agents. The method is validatedexperimentally on two academic examples.

Consensus analysis of large-scale nonlinear homogeneous multi-agent formations with polynomial dynamics