A new measure of non-linearity, that is captured by two linear systems, is proposed to quantify the size of the non-linearity in the input/output behaviour of SISO non-linear systems. As such, the controller design for the non-linear system is simplified to the design of a controller for these two linear systems. It is also shown that when Hammerstein and Wiener models are involved, the controller design for these two structures are equivalent if the linear dynamic term is stable. Two examples, a numerical example and a non-linear system characterized by a time-delay and a variable gain are used to demonstrate these concepts.