Laplacian Controllability and Observability of Multi-Agent Systems: Recent Advances in Tree Graphs

Laplacian controllability and observability of a consensus network is a widely considered topic in the area of multi-agent systems, complex networks, and large-scale systems. In this paper, this problem is addressed when the communication among nodes is described through a starlike tree topology. After a brief description of the mathematical setting of the problem adopted in a wide number of multi-agent systems engineering applications, some novel results are drawn based on node positions within the network only. The resulting methods are graphical and thus effective and exempt from numerical errors, and the final algorithm is provided to perform the analysis by machine computation. Several examples are provided to show the effectiveness of the algorithm proposed.