On the consensus problem with positivity constraints

In this paper we investigate the consensus problem for multi-agent systems, under the assumptions that the agents are homogeneous and described by a single-input positive state-space model, the mutual interactions are cooperative, and the static state-feedback law that each agent adopts to achieve consensus preserves the positivity of the overall system. Conditions that are either necessary or sufficient for the solvability of the positive consensus problem are provided. Under certain additional assumptions on the agents dynamics, equivalent conditions are derived. Several examples illustrate the paper results.