A Graph-Theoretic Approach to the $\mathcal{H}_{\infty}$ Performance of Dynamical Systems on Directed and Undirected Networks
Abstract
We study a graph-theoretic approach to the performance of leader following consensus dynamics on directed and undirected graphs. We first provide graph-theoretic bounds on the system norm of the leader following dynamics and show the tightness of the proposed bounds. Then, we discuss the relation between the system 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 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 performance of the system.
Keywords
Cite
@article{arxiv.1804.10483,
title = {A Graph-Theoretic Approach to the $\mathcal{H}_{\infty}$ Performance of Dynamical Systems on Directed and Undirected Networks},
author = {Mohammad Pirani and Henrik Sandberg and Karl Henrik Johansson},
journal= {arXiv preprint arXiv:1804.10483},
year = {2018}
}