Positive Consensus of Directed Multi-Agent Systems

Abstract

This paper investigates the positive consensus problem of multi-agent systems with directed communication topologies where all the agents have identical continuous-time positive linear dynamics. Existing works of such problem mainly focus on the case where the networked communication topologies are of either undirected and incomplete graphs, or strongly connected directed graphs. In stark contrast to them, we study the problem in which the communication topologies of the networked system are described by directed graphs each containing a spanning tree which is a more general and new scenario due to the interplay between the eigenvalues of the Laplacian matrix and the controller gains. Based on the existing results in spectral graph theory and positive linear systems theory, several necessary and sufficient conditions on the positive consensus of the directed multi-agent system are derived through using linear matrix inequality techniques. Then a primal-dual iterative algorithm is developed for computation and finally several numerical simulations are provided to illustrate the effectiveness of the proposed theoretical results.