On consensus of nonlinear multi-agent systems under directed interaction topologies

In a consensus problem, autonomous agents constituting a dynamical system communicate with one another to reach agreement on certain quantities of interest. By merging control theory and spectral graph theory, we generalize the previous consensus problems under nonlinear protocols for networks with undirected graphs to directed graphs. We prove that, when the nonlinear protocol is strictly increasing, consensus can be achieved if and only if the underlying directed interaction graph has a spanning tree. Numerical examples are taken to show the effectiveness of our theoretical results.