AN INTEGRAL CONNECTIVITY CONDITION FOR MULTI-EQUILIBRIA CONSENSUS IN NETWORKS EVOLVING OVER UNDIRECTED GRAPHS

Abstract

In this paper, we study the multi-equilibrium consensus problem for a time-varying network of n agents where the agents are modeled as integrators. Instead of the joint connectivity condition which is widely used in the literature, we propose an integral K connectivity condition that allows us to examine the network through a constant matrix. Based on this new concept, we present necessary and sufficient conditions on networks modeled with undirected graphs so that multi-equilibrium consensus states are achieved. Theoretical results are verified by numerical simulations.