Mitigation of complex behavior over networked systems: Analysis of spatially invariant structures

Jing Wang, Nicola Elia

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


In this paper, we consider a simple distributed averaging system, which incorporates various communication constraints including delays, noise, and link failures. It has been shown in Wang and Elia (2012) that such networked system generates a collective Lévy flight behavior when part of the system loses mean square (MS) stability. We focus on spatially invariant architectures to gain more insights into how model parameters affect emergence of this complex scale-invariant behavior, and to seek structures robust to communication constraints. Specifically, we develop a computational expression for checking MS stability, which is scalable with the number of unreliable links. We derive the closed form formulas from this expression in the limiting case of zero and large delays, and in the case of large number of nodes. In the limit of large delays, we derive various results that are independent of the network size and its specific interconnections. We find that small inter-agent coupling improves the robustness of the system. Networks with larger connectivity tend to be more fragile in the presence of fading connections for fixed inter-agent coupling. That gossiping improves the robustness and that the lattice is the most robust among the spatially invariant systems with generalized circulant interconnections.

Original languageEnglish (US)
Pages (from-to)1626-1638
Number of pages13
Issue number6
StatePublished - Jun 2013
Externally publishedYes

Bibliographical note

Funding Information:
This research has been supported by NSF under grant number ECS-0524689 and partially supported by NSF under grant number ECS-0901846 . The material in this paper was partially presented at the 47th IEEE Conference on Decision and Control (CDC), December 9–11, 2008, Cancun, Mexico. This paper was recommended for publication in revised form by Associate Editor Xiaobo Tan under the direction of Editor Miroslav Krstic.

Copyright 2013 Elsevier B.V., All rights reserved.


  • Complex systems
  • Consensus
  • Distributed averaging
  • Hyper-jump diffusion
  • Lévy flights
  • Mean square stability
  • Networked systems
  • Scale invariance


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