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Commonly, controllers for linear parameter-varying (LPV) systems are designed in continuous time using a linear fractional representation (LFR) of the plant. However, the resulting controllers are implemented on digital hardware. Furthermore, discrete-time LPV synthesis approaches require a discrete-time model of the plant which is often derived from a continuous-time first-principle model. Existing discretization approaches for LFRs describing LPV systems suffer from disadvantages like the possibility of serious approximation errors, issues of complexity, etc. To explore the disadvantages, existing discretization methods are reviewed and novel approaches are derived to overcome them. The proposed and existing methods are compared and analyzed in terms of approximation error, considering ideal zero-order hold actuation and sampling. Criteria to choose appropriate sampling times with respect to the investigated methods are also presented. The proposed discretization methods are tested and compared both on a simulation example and on the electronic throttle control problem of a race motorcycle.