We are now dealing with a hybrid system in which the plant is analog
(related to the Laplace transform) whereas the controler is digital
(related to the Z-transform). The goal is to deal with the complex
frequency reponse function H of the system, where H is either a
function of s 
or of z 
depending on which component
of the system we are dealing with: the plant or the controller. Using
the bilinear transform, we are able to ``jump'' from one domain to the
other and then have a consistent system which can be designed in the
analog domain and then treated back in the discrete domain.