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Mathematical Control Theory I pp 321–341Cite as

Network Topology and Synchronization of Systems with Linear Time-Delayed Coupling

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Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 461))

Abstract

We consider networks of square input–output systems that interact via linear, time-delayed coupling functions. For given system dynamics, we give conditions for the construction of a (local, global) synchronization diagram. We show that a condition for (local, global) synchronization is that the coupling strength and time-delay are contained in the intersection of scaled copies of the (local, global) synchronization diagram, where the scaling factors are the nonzero eigenvalues of the symmetric Laplacian matrix.

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Author information

Authors and Affiliations

  1. Institute for Complex Molecular Systems and Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Erik Steur

  2. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, The Netherlands

    Henk Nijmeijer

Authors
  1. Erik Steur
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  2. Henk Nijmeijer
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Correspondence to Henk Nijmeijer .

Editor information

Editors and Affiliations

  1. Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands

    M. Kanat Camlibel

  2. Department of Electrical, Computer and Systems Engineering, Rensselaer Polytechnic Institute, Troy, New York, USA

    A. Agung Julius

  3. Department of Electrical Engineering, Indian Institute of Technology, Chennai, Tamil Nadu, India

    Ramkrishna Pasumarthy

  4. Engineering and Technology Institute Groningen, University of Groningen, Groningen, The Netherlands

    Jacquelien M.A. Scherpen

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Steur, E., Nijmeijer, H. (2015). Network Topology and Synchronization of Systems with Linear Time-Delayed Coupling. In: Camlibel, M., Julius, A., Pasumarthy, R., Scherpen, J. (eds) Mathematical Control Theory I. Lecture Notes in Control and Information Sciences, vol 461. Springer, Cham. https://doi.org/10.1007/978-3-319-20988-3_17

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  • DOI: https://doi.org/10.1007/978-3-319-20988-3_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-20987-6

  • Online ISBN: 978-3-319-20988-3

  • eBook Packages: EngineeringEngineering (R0)

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