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Delays and Interconnections: Methodology, Algorithms and Applications pp 65–81Cite as

ISS-Stabilization of Delayed Neural Fields by Small-Gain Arguments

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Part of the Advances in Delays and Dynamics book series (ADVSDD,volume 10)

Abstract

This chapter addresses the robust stabilization of neuronal populations modeled as delayed neural fields. These models are integro-differential equations representing the spatio-temporal activity of cerebral structures and take into account the non-instantaneous communication between neurons. It is assumed that the stimulation signal impacts only a subpopulation, referred to as the “controlled” population. We show that, if the synaptic coupling within the “uncontrolled” population is below some explicit threshold, then a proportional feedback relying only on measurements of the controlled subpopulation activity succeeds in ensuring robust stability of the overall population. These theoretical developments rely on an extension of the input-to-state stability (ISS) property, and associated small-gain results, to spatio-temporal delayed dynamics.

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  • DOI: 10.1007/978-3-030-11554-8_5
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Author information

Authors and Affiliations

  1. L2S - CentraleSupélec - Université Paris Sud - CNRS, University of Paris Saclay, Gif sur Yvette, France

    Antoine Chaillet & Georgios Is. Detorakis

  2. APHP H. Mondor Hospital, INSERM U955 équipe 14, University Paris Est - Faculté de Médcine, Crétil, France

    Stéphane Palfi & Suhan Senova

Authors
  1. Antoine Chaillet
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  2. Georgios Is. Detorakis
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  3. Stéphane Palfi
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  4. Suhan Senova
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Corresponding author

Correspondence to Antoine Chaillet .

Editor information

Editors and Affiliations

  1. Laboratoire des Signaux et Systèmes, CNRS-CentraleSupèlec-Université Paris-Saclay, Gif-sur-Yvette, France

    Prof. Giorgio Valmorbida

  2. Laboratoire d’Analyse et d’Architecture de Systèmes-CNRS, Toulouse, France

    Dr. Alexandre Seuret

  3. Laboratoire des Signaux et Systèmes, CNRS-CentraleSupèlec-Université Paris-Saclay, Gif-sur-Yvette, France

    Islam Boussaada

  4. Mechanical and Industrial Engineering, Northeastern University, Boston, MA, USA

    Prof. Rifat Sipahi

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Chaillet, A., Detorakis, G.I., Palfi, S., Senova, S. (2019). ISS-Stabilization of Delayed Neural Fields by Small-Gain Arguments. In: Valmorbida, G., Seuret, A., Boussaada, I., Sipahi, R. (eds) Delays and Interconnections: Methodology, Algorithms and Applications. Advances in Delays and Dynamics, vol 10. Springer, Cham. https://doi.org/10.1007/978-3-030-11554-8_5

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