Complexities and Performance Limitations in Growing Time-Delay Noisy Linear Consensus Networks

This work investigates topology design for optimal performance in time-delay noisy networks. Performance of the network is measured by the square of the system's H2-norm. The focus of this paper is on adding new interconnections to enhance performance of the time-delay first-order connected consensus network. We discuss complexity of topology optimization for delayed networks and develop two practical methods to tackle the combinatorial eigenvalue problem without exhaustive search or eigen-decomposition. Furthermore, we compare these methods and discuss their degrees of optimality.