  This paper focuses on the systems theory of bilinear dynamical systems using
the Volterra series representation. The main contributions are threefold.
First, we gain an input-output representation in the frequency domain, where
the Laplace transform of the kernels can indeed be interpreted as transfer
functions. Then, we derive the response of bilinear systems to a nascent delta
function in time domain, i.e. the impulse response of bilinear systems.
Finally, we study the relationships between this novel impulse response and the
well-known Volterra kernels and adjust those to be compatible to the impulse
response.
