The signal resolution is increased proportional with sampling rate .. For simplification, it can be considered as a continuous, but at the same time it is discrete.

Also, when implementing the simulated results in a digital hardware, then most important thing is if your that hardware can deal with high sampling rate or not!

If the sampling period is very small ( of the order 10*** (-alpha) , alpha being sufficiently large related to the dominant time constants) then the discrete version can reflect the continuous-time one in many cases. On the other hand, if the continuous-time system is being forced by a continuous-time input which is piecewise constant ( the length of each constant input portion equalizing the sampling period) then the output and state responses at sampling points are exactly coincident with the corresponding discrete sequences. In the intersample periods, it happens the following:

a) If the discrete -time model is a purely discrete mathematical one ( for instance, based on z- transforms or time responses just at sampling points) then there is no exact information about the values of the state/output signals. However, if the sampling period is sufficiently small , then the signal plots provided by the simulator with the corresponding automatic interpolation can give a very close information of the whole signals. This can be sufficient to display most of simulations

b) If a whole state-space discrete model ( input is piecewise contant by a zero-order- hold but the sate and output are generated at any sampling instant , or the modified z- transform with the z- transform m- parameter ranging from "zero" to "one") are used then the solutions in the intersampling period are also exact.

High sampling rate chosen for a discretized version of the continuous plant makes the system near to the continuous . but high sampling rate increases the cost of the hardware.