Distributed Consensus with Multi-Equilibria in Directed Networks

This paper studies the multi-equilibria consensus problem for discrete-time multi-agent networks with fixed communication topologies. The agents are assumed to use the traditional distributed averaging based consensus algorithm that relies on neighbor information exchange. Given the graph of the network, two new notions of primary and secondary layer subgraphs are introduced, which are subsequently used in determining the number of consensus equilibria. Numerical examples are provided to illustrate the results.