This paper presents a systematic methodology to deal with variable transport delays by constructing a new discrete domain where the delay becomes fixed (a difference of samples). The Euler transformation is used to change from the continuous-time domain to this special discrete domain depending on the same variable as the transport delay. After this transformation, the model becomes nonlinear and the Takagi-Sugeno fuzzy representation is used to handle the nonlinearities. To highlight and illustrate the efficiency of the proposed methodology, an LMI based controller design is used to control a conveyor belt with variable transport delay