Used in process control to represent the relationship between the output to input signal from and to a process in which the differential equations used to describe the signals as functions of time have been transformed using Laplace transforms. Laplace transforms are used to simplify the calculations since differential equations do not readily enable the relationship between the output to the input to be discerned. The transformation is said to be from the time domain to the s-domain. If the input is y(t) and the output is y(t) then the transformed function G(s) is:
Capital letters are used for variables in the s-domain and lower-case letters for the time domain.