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This technical note investigates the positive consensus problem of multiagent systems with directed communication topologies, where all the agents have identical continuous-time positive linear dynamics. Existing works of such a problem mainly focus on the case, where networked communication topologies are of either undirected and incomplete graphs, or strongly connected directed graphs. In contrast to them, we study this problem in which the communication topologies of the multiagent 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 positive consensus of the directed multiagent system are derived through using linear matrix inequality techniques. A primal-dual iterative algorithm is developed for the computation of solutions. Finally, several numerical simulations are provided to illustrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This note deals with the positivity-preserving consensus problem for undirected positive multiagent systems. The case that all agents have identical positive state-space models with multiple inputs is investigated. Using positive systems theory and analyzing the properties of the overall closed-loop system, positivity-preserving consensus conditions are derived. In order to preserve the positivity property of the agents, two conditions for positivity-preserving consensus are obtained. In contrast to some existing works that only give sufficient conditions for the solution, necessary and sufficient conditions are provided in this note. Then, the corresponding algorithm is developed for solution. Simulations are used to illustrate the effectiveness of the theoretical results and proposed algorithm. [ABSTRACT FROM AUTHOR]