Dependence of delay margin on network topology: Single delay case

Abstract

This article studies the indirect relationship between the delay margin τ * of coupled systems and different graphs these systems form via their different topologies. A four-agent linear time invariant (LTI) consensus dynamics is taken as a benchmark problem with a single delay τ and second-order agent dynamics. In this problem, six different topologies exist without disconnecting an agent from all others. We first start with CTCR to reveal the delay margin τ *. We next investigate how τ * is affected as one graph transitions to another when some links between the agents weaken and vanish. This line of research is recently growing and new results along these lines promise delay-tolerant topology design for coupled dynamical systems with delays. © 2012 Springer-Verlag GmbH Berlin Heidelberg.