On Performance of Time-Delay Linear Consensus Networks with Directed Interconnection Topologies

We study performance of noisy linear timeinvariant (LTI) consensus networks in the presence of timedelay with directed graph topologies. The H-2-norm squared of the network is adopted as the performance measure. One of our main results provides an explicit expression for the H-2-norm of directed networks with normal Laplacian matrices. This expression is in terms of Laplacian eigenvalues and timedelay. Furthermore, we exploit topology of some well-known graphs and show how their H-2-norm scale with network size and time delay. It is also proven that H-2-norm of a directed network with normal Laplacian is an increasing function of time-delay.