Performance Measure of Hierarchical Structures for Multi-agent Systems

This paper investigates the robustness of linear consensus networks which are designed under a hierarchical scheme based on Cartesian product. For robustness analysis, consensus networks are subjected to additive white Gaussian noise. To quantify the robustness of the network, we use H-2-norm: the square root of the expected value of the steady state dispersion of network states. We compare several classes of undirected and directed graph topologies. We show that the hierarchical structures, designed under the Cartesian product-based hierarchy, outperform the single-layer structures in terms of robustness. We provide simulations to support the analytical results presented in this paper.