[Scilab-users] Something wrong with the conversion from frequency domain to time domain?

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moi moi
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[Scilab-users] Something wrong with the conversion from frequency domain to time domain?

Hello,

I'm trying to convert a function from continuous time to discrete time.

There is following continuous time transfer function.
Gc = 1 / (1 + 0.1*s)

I converted to continuous time state space.
Gsl = tf2ss(Gc)

and converted to discrete time state space with dt = 0.001 sec.
Gsd = dscr(Gsl, 0.001)

Finally, converted to discrete time transfer function.
Gd = ss2tf(Gsd)

The result is following:
Gd  =
      0.0099502
    ---------------
    -0.9900498 + z

I converted these function with the inverse Laplace transform and the
inverse z transform.

Inverse Laplace transform:
L^-1[Gc] = y(t) = 10*e^(-10*t)

Inverse Z transform:
Apply 'z^-1' to numerator and denominator.
Z^-1[Gd] = 0.0099502 * z^-1 / (-0.9900498 * z^-1 + 1)

Apply the inverse z transform formula 'L^-1[1/(1 - az)] = a^n * u[n]'
and 'L^-1[z^-k * F] = D^k * F'.
Z^-1[Gd] = 0.0099502 * D^-1 * 0.9900498^n * u[n];
     y[n] = 0.0099502 * 0.9900498^[n-1] * u[n];

I calculated these expressions in Excel.

t    y(t)        y[n]
0    10          0.0099502
1    9.900498337 0.0099502
2    9.801986733 0.009851194
3    9.704455335 0.009753172
4    9.607894392 0.009656126
5    9.512294245 0.009560046
6    9.417645336 0.009464921
7    9.323938199 0.009370744
8    9.231163464 0.009277503
9    9.139311853 0.00918519

The numerical value is greatly different.
Did I mistake something?

Thanks in advance.

moi
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