Existence of an equilibrium for 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

In [2], the authors study the stabilization of a class of delayed neural fields through output proportional feedback. They provide a condition under which the resulting closed-loop system is input-to-state stable (ISS). However, a key assumption in that paper is the existence of an equilibrium for the closed-loop system. We show here that such an equilibrium does exist if 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 neural fields under output proportional feedback. 2022. ⟨hal-03589737v2⟩