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In this paper we propose a novel method to establish stability and, inaddition, convergence to a consensus state for a class of discrete-timeMulti-Agent System (MAS) evolving according to nonlinear heterogeneous localinteraction rules which is not based on Lyapunov function arguments. Inparticular, we focus on a class of discrete-time MASs whose global dynamics canbe represented by sub-homogeneous and order-preserving nonlinear maps. Thispaper directly generalizes results for sub-homogeneous and order-preservinglinear maps which are shown to be the counterpart to stochastic matrices thanksto nonlinear Perron-Frobenius theory. We provide sufficient conditions on thestructure of local interaction rules among agents to establish convergence to afixed point and study the consensus problem in this generalized framework as aparticular case. Examples to show the effectiveness of the method are providedto corroborate the theoretical analysis.

A Nonlinear Perron-Frobenius Approach for Stability and Consensus of Discrete-Time Multi-Agent Systems