we consider all the initial conditions are zero because After taking Laplace Transform of the whole system, x(t) becomes X(s), y(t) becomes Y(s). In the above system, the input is x (t) and the output is y(t). The transfer function of the LTI system is the ratio of the Laplace transform of output to the Laplace transform of input of the system by assuming all the initial conditions are zero. Hadoop, Data Science, Statistics & others Definition of Transfer Functions in Matlab