Positivity-Preserving Consensus of Homogeneous Multiagent Systems

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.