  The paper introduces a kernel-based framework to model and identify
time-invariant systems with the fading memory property. The key departure from
the previous literature is to bypass the state-space representation of the
model. Instead, a kernel representation is used to directly model the memory
functional that maps past inputs to the present output. We explore the
versatility of this approach to encode important system properties in the
hyperparameters of the kernel. The approach is illustrated on the Hodgkin and
Huxley model of neuronal excitability.
