Reaching nonlinear consensus via non-autonomous polynomial stochastic operators

This paper is a continuation of our previous studies on nonlinear consensus which uni�es and generalizes all previous results. We consider a nonlinear protocol for a structured time-varying synchronous multi-agent system. We present an opinion sharing dynamics of the multi-agent system as a trajectory of non-autonomous polynomial stochastic operators associated with multidimensional stochastic hyper-matrices. We show that the multi-agent system eventually reaches to a nonlinear consensus if either one of the following two conditions is satisfied: (i) every member of the group people has a positive subjective distribution on the given task after some revision steps or (ii) all entries of some multidimensional stochastic hyper-matrix are positive