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.