Jesus,

The reason your simulations take so long to run is that you have some terms with infinite precision (Pi). If you numericise the transfer function it runs a thousand times faster.

    ToDiscreteTimeModel[N[AffineSS], dt, z]

putting the third argument, z, means that you want the discrete variable to be "z"

The default conversion to digital is not stable unless you lower your time step. I got reasonable short duration results with

    dt = 1/50/100000;

Your u2 definition does not agree with the continuous definition. It should be:

    u2 = Table[0., {z, 0, np}];

The simulation takes a long time because we are using such a tiny time step to maintain stability. np =200,000 works and exactly matches the continuous data:

    Show[ListPlot[SimuDT[[1, All]], DataRange -> {0, np*dt}, 
      PlotStyle -> Red], Plot[SimuAffine[[1]], {t, 0, np*dt}]]

You should use more stable conversion options for ToDiscreteTimeModel[]. The options are put in like this: Method->"ForwardRectangularRule"

For example:

DTAffineSS = 
 ToDiscreteTimeModel[N[AffineSS], dt, z, 
  Method -> "ForwardRectangularRule"]

The options are {"ForwardRectangularRule", "BackwardRectangularRule", "BilinearTransform", "ZeroOrderHold", "FirstOrderHold"}

Unfortunately, there seems to be a bug for all options except ForwardRectangularRule. I would report this to Wolfram. The other options should work (and be more stable allowing for a larger timestep)

I hope this helps.

Regards

Neil