This paper concerns the consensus analysis of multiagent systems made of the interconnection of identical nonlinear agents interacting with one another through an undirected and connected graph topology. Drawing inspiration from the theory of linear “decomposable systems,” we provide a method for proving the convergence (or consensus) of such multiagent sytems in the case of polynomial dynamics. The method is based on a numerical test, namely a set of linear matrix inequalities providing sufficient conditions for the convergence. We also show that the use of a generalized version of the famous Kalman‐Yakubovic‐Popov lemma allows the development of a linear matrix inequalities test whose size does not directly depend on the number of agents. The method is validated in simulation on three examples, which also show how the numerical test can be used to properly tune a controller.