Existence of an equilibrium for delayed neural fields under output proportional feedback

Lucas Brivadis (1) , Cyprien Tamekue (1) , Antoine Chaillet (1) , Jean Auriol (1)

1 L2S - Laboratoire des signaux et systèmes

Recently, [2] proved that the closed-loop system resulting from the output proportional feedback stabilization of a class of delayed neural fields is input-to-state stable (ISS) for sufficiently high gain, subject to the existence of an equilibrium point for the closed-loop system. In the present paper, we show that a sufficient condition for such an equilibrium to exist is that the activation functions are bounded.

Mots clés: fixed point; delayed neural fields; robust stabilization; input-to-state stability; spatiotemporal delayed systems

Domaines: Optimisation et contrôle [math.OC]; Automatique / Robotique

Lucas Brivadis, Cyprien Tamekue, Antoine Chaillet, Jean Auriol. Existence of an equilibrium for delayed neural fields under output proportional feedback. Automatica, 2023, ⟨10.1016/j.automatica.2023.110909⟩. ⟨hal-03589737v3⟩