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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 book series: Advances in Delays and Dynamics ((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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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

    Giorgio Valmorbida

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

    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

    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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