Krause Mean Processes Generated by Off-Diagonally Uniformly Positive Nonautonomous Stochastic Hyper-Matrices

The notion of consensus through repeated averaging was first introduced by DeGroot in the context of structured, time-invariant and synchronous environments. Since then, consensus has emerged as a prevalent phenomenon in multi-agent systems and has been extensively studied in a diverse range of fields, including biology, physics, control engineering, and social science. The Krause mean process is a generalized model of opinion dynamics among many agents that represents opinions as vectors. In this work, we investigate an opinion sharing dynamics in the multi-agent system by means of Krause mean processes which are generated by doubly stochastic hyper-matrices. This is arguably a feasible generalization of the classical DeGroot and Chatterjee-Seneta models from square stochastic matrices to higher-order stochastic hyper-matrices. We then demonstrate how consensus can be achieved in the multi-agent system when doubly stochastic hyper-matrices are off-diagonally uniformly positive.