Mean Square Limitations of Spatially Invariant Networked Systems

Nicola Elia, Jing Wang, Xu Ma

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations


In this chapter, we summarize some of our recent results on spatially invariant networked systems. We study the effects of unreliable communication on these systems' stability and performance. Because of their special structure, the quantities that characterize the limitations of these systems can be computed more easily. In particular, we focus on Mean Square stability and performance, and investigate network architectures, which are more robust and better performing. We consider multi-agent networked systems where the communication links are unreliable and stochastically dropout. Spatial invariance leads to a simplified computation of the MS stability limitation, and allows us to derive an uncertainty conservation law enjoyed by such systems. We then focus on distributed averaging systems, for which the loss of Mean Square stability leads to the emergence of certain complex behavior related to Lévy flights. We present closed form formulae characterizing Mean Square stability and performance in the presence of unreliable communication among the nodes. Finally, we study Mean square performance in the presence of unreliable links. Our results allow to characterize the interplay between Mean Square performance and stability of torus networks of different dimensions.

Original languageEnglish (US)
Title of host publicationControl of Cyber-Physical Systems - Workshop Held at The Johns Hopkins University
PublisherSpringer Verlag
Number of pages22
ISBN (Print)9783319011585
StatePublished - 2013
Externally publishedYes
EventWorkshop on Control of Cyber-Physical Systems, CPS 2013 - Baltimore, MD, United States
Duration: Mar 20 2013Mar 21 2013

Publication series

NameLecture Notes in Control and Information Sciences
Volume449 LNCIS
ISSN (Print)0170-8643


OtherWorkshop on Control of Cyber-Physical Systems, CPS 2013
Country/TerritoryUnited States
CityBaltimore, MD


  • Mean Square performance
  • Mean Square stability
  • complex systems
  • packet-drop networks
  • spatially invariant systems


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