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If a system has the following step response:

$y(t) = 1 - [A e^{(−t/T1)} + (1-A) e^{(−t/T2)}]$

and I know the values of A, T1 and T2, can I transform this to a discrete-time IIR filter analytically? If there is no analytical solution, is it possible to say how many poles/zeros the IIR filter should have?

I've done it numerically by using the Prony's method on the impulse response, but I'm hoping there is a more direct way.

If a system has the following step response:

$$\begin{align} y(t) &= 1 - \Big(A e^{−t/T_1} + (1-A) e^{−t/T_2}\Big) \\ &= 1 - A e^{−t/T_1} - (1-A) e^{−t/T_2} \\ \end{align}$$

and I know the values of $A$, $T_1$ and $T_2$, can I transform this to a discrete-time IIR filter analytically? If there is no analytical solution, is it possible to say how many poles/zeros the IIR filter should have?

I've done it numerically by using the Prony's method on the impulse response, but I'm hoping there is a more direct way.

If a system has the following step response:

$y(t) = 1 - [A e^{(−t/T1)} + (1-A) e^{(−t/T2)}]$

and I know the values of A, T1 and T2, can I transform this to an IIR filter analytically? If there is no analytical solution, is it possible to say how many poles/zeros the IIR should have?

I've done it numerically by using the Prony method on the impulse response, but I'm hoping there is a more direct way.

If a system has the following step response:

$y(t) = 1 - [A e^{(−t/T1)} + (1-A) e^{(−t/T2)}]$

and I know the values of A, T1 and T2, can I transform this to a discrete-time IIR filter analytically? If there is no analytical solution, is it possible to say how many poles/zeros the IIR filter should have?

I've done it numerically by using the Prony's method on the impulse response, but I'm hoping there is a more direct way.

If a system has the following step response:

$y(t) = 1 - [A e^{(−t/T1)} + (1-A) e^{(−t/T2)}]$

and I know the values of A, T1 and T2, can I transform this to an IIR filter analytically? If there is no exact solution, is it possible to say how many poles/zeros the IIR should have?

I've done it numerically by using the Prony method on the impulse response, but I'm hoping there is a more direct way.

If a system has the following step response:

$y(t) = 1 - [A e^{(−t/T1)} + (1-A) e^{(−t/T2)}]$

and I know the values of A, T1 and T2, can I transform this to an IIR filter analytically? If there is no analytical solution, is it possible to say how many poles/zeros the IIR should have?

I've done it numerically by using the Prony method on the impulse response, but I'm hoping there is a more direct way.