The main objective in this paper is to capture the indirect relationship between the delay margin τ* of coupled systems and different graphs G these systems form via their different topologies, τ* = τ*(G). 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 possible topologies with graphs G1,...,G6 exist without disconnecting an agent from all others. To achieve the objectives of the paper, we start with a recently introduced stability analysis technique called Advanced Clustering with Frequency Sweeping (ACFS) and reveal the delay margin τ*, that is, the largest delay that the consensus dynamics can withstand without loosing stability. We next investigate how τ* is affected as one graph transitions to another when some links between the agents weaken and eventually vanish. Finally, the damping effects to τ* and the graph transitions are studied and discussed with comparisons. This line of research has been recently growing and new results along these lines promise delay-independent, robust and delay-tolerant topology design for coupled delayed dynamical systems.
stability, topology, delay margin, delay tolerant network
Copyright © IFAC 2010
Qiao, Wei and Sipahi, Rifat, "Dependence of delay margin on network topology: single delay case" (2010). Mechanical and Industrial Engineering Faculty Publications. Paper 48.
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