Series-parallel networks are a class of graphs on which many NP-hard problems have tractable solutions. In this paper, we examine performance measures on leader-follower consensus on series-parallel networks. We show that a distributed computation of the $\mathcal{ H}_2$ norm can be done efficiently on this system by exploiting a decomposition of the network into atomic elements and composition rules. Lastly, we examine the problem of adaptively re-weighting the network to optimize the $\mathcal{ H}_2$ norm, and show that it can be done with similar complexity.
Categories: math.OC