Fast consensus in a large-scale multi-agent system with directed graphs using time-delayed measurements.

This article is on fast-consensus reaching in a class of multi-agent systems (MAS). We present an analytical approach to tune controllers for the agents based on the premise that delayed measurements in the controller can be preferable to standard controllers relying only on current measurements. Controller tuning in this setting is however challenging due to the presence of delays. To tackle this problem, we propose an analytic geometry approach. The key contribution is that the tuning can be implemented for complex eigenvalues of the arising graph Laplacian of the network, complementing the current state of the art, which is limited to real eigenvalues. Results, therefore, extend our knowledge beyond symmetric graphs and enable the study of the MAS under directed graphs. This article is part of the theme issue 'Nonlinear dynamics of delay systems'.