Observer-Based Positive Edge Consensus of Multi-agent Systems on Directed Graphs

This paper explores positive edge-consensus in directed networks with spanning trees using output feedback protocols. First, a novel positive system observer is proposed, which introduces a parameter to enhance the design freedom of the observer. Furthermore, using positive system theory and graph theory, sufficient conditions are proposed and the sufficient conditions based solely on the network’s edge count. Specifically, an optimized bound is given for the eigenvalue of the Laplacian matrix, and an improved consensus and non-negative condition is obtained. Finally, the effectiveness of the proposed control protocol is verified utilizing numerical simulations.