Performance Analysis and Optimal Design of Time-Delay Directed Consensus Networks

The $\mathcal {H}_2$ performance of a class of noisy time-delay consensus networks with directed interconnection topologies is considered. For networks with normal Laplacian, we derive a closed-form expression for the performance measure and study its functional properties. The scaling properties of the $\mathcal {H}_2$-norm are investigated for some families of networks. Finally, the problem of tuning feedback gains of a network with fixed topology in order to improve its performance is considered. Our proposed design method can handle networks with a thousand nodes.