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

Abstract

In this paper, we study the multi-equilibria 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 multiequilibrium consensus states are achieved. Theoretical results are verified by numerical simulations