A Graph-Theoretic Approach to the H∞ Performance of Dynamical Systems on Directed and Undirected Networks
Abstract
We study a graph-theoretic approach to the H∞ performance of leader following consensus dynamics on directed and undirected graphs. We first provide graph-theoretic bounds on the system H∞ norm of the leader following dynamics and show the tightness of the proposed bounds. Then, we discuss the relation between the system H∞ norm for directed and undirected networks for specific classes of graphs, i.e., balanced digraphs and directed trees. Moreover, we investigate the effects of adding directed edges to a directed tree on the resulting system H∞ norm. In the end, we apply these theoretical results to a reference velocity tracking problem in a platoon of connected vehicles and discuss the effect of the location of the leading vehicle on the overall H∞ performance of the system.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.