Lap time simulation is one of the most powerful tools for evaluating design proposals in motorsport engineering. In particular, transient simulations play an important role as the ultimate and more accurate approach than other static or quasi-steady-state methodologies. In this paper, first, the method to transform the differential equations of a system into a formally linear continuous and then discrete state-space representation, particularised for a seven-degree-of-freedom suspension and a transient cornering model, is proposed. The use of time-variant coefficients in the matrices of the model will allow the non-linear and time-variant characteristics of these systems to be described. Second, in the case of the transient cornering model, this representation is translated into a transfer function in order to apply a discrete control strategy such as a finite-time strategy or a predictive strategy for an adaptive ideal driver. It was found that the calculation methodology described above can be successfully applied with a more than acceptable degree of accuracy according to comparison with the results using other mechanical or numerical software (ADAMS or Simulink). It was also observed that the use of the curvature of the track as a reference in the control closed loop is sufficiently accurate to force the car to follow the target path closely. Furthermore, both predictive control and finite-time control (including integration) provide excellent results with a smooth response of the steering input. Many lap time simulators are language specific; however, the methodology proposed in this paper will run in most programming languages.