Journal of Global Optimization

, Volume 67, Issue 1–2, pp 187–205 | Cite as

On Laplacian spectra of parametric families of closely connected networks with application to cooperative control

  • Alla Kammerdiner
  • Alexander Veremyev
  • Eduardo Pasiliao


In this paper, we introduce mathematical models for studying a supernetwork that is comprised of closely connected groups of subnetworks. For several related classes of such supernetworks, we explicitly derive an analytical representation of their Laplacian spectra. This work is motivated by an application of spectral graph theory in cooperative control of multi-agent networked systems. Specifically, we apply our graph-theoretic results to establish bounds on the speed of convergence and the communication time-delay for solving the average-consensus problem by a supernetwork of clusters of integrator agents.


Supernetworks Parametric families of graphs Laplacian spectra Average-consensus problem 



The first author gratefully acknowledges the support provided by the U.S. Air Force Research Laboratory (AFRL) Summer Faculty Fellowship Program (SFFP).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Alla Kammerdiner
    • 1
  • Alexander Veremyev
    • 2
  • Eduardo Pasiliao
    • 2
  1. 1.New Mexico State UniversityLas CrucesUSA
  2. 2.Air Force Research LaboratoryMunitions DirectorateEglin AFBUSA

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