H∞ Analysis and Synthesis of Time-Scaled and Weighted Edge Consensus Networks

This work focuses on networks of single-integrator time-scaled agents interconnected through weighted edges, in which both the agents and their edges are affected by zero-mean Gaussian noise. The noise impact is measured using the H ∞ -norm of the resulting dynamical system. We propose a method to convexify the computation of the previously-mentioned H ∞ - norm in terms of the weights and time scales of the graph. Furthermore, we provide a convex synthesis method to minimize the norm based on the variable weights and time scales. We cover two performance indices based on the configurations of the system’s output: using the spanning tree edge states, or alongside the co-tree edge states. A numerical example illustrates the proposed method.