  This paper provides control-oriented delay-based modeling of a one-layer
neural network of Hopfield-type subject to an external input designed as
delayed feedback. The specificity of such a model is that it makes the
considered neuron less susceptible to seizure caused by its inherent dynamic
instability. This modeling exploits a recently set partial pole placement for
linear functional differential equations, which relies on the coexistence of
real spectral values, allowing the explicit prescription of the closed-loop
solution's exponential decay. The proposed framework improves some pioneering
and scarce results from the literature on the characterization of the exact
solution's exponential decay when a simple real spectral value exists. Indeed,
it improves neural stability when the inherent dynamic is stable and provides
insights into the design of a one-layer neural network that can be stabilized
exponentially with delayed feedback and with a prescribed decay rate regardless
of whether the inherent neuron dynamic is stable or unstable.
