Finding Impulse Transfer Function with Impulse Invariant Method

[maxiking]

Homework Statement

Transfer functions of the continuous compensation links are given as follows. Find the impulse transfer functions of the digital compensation links using the impulse invariant method.

$\frac{a}{s+a}$

I don't know how to solve the problem correctly

Homework Equations

D(z)=Z[D(s)]

The Attempt at a Solution

d(t) = ae^-at
D(z)=$\frac{az}{z-e^(-at)}$

 

[RoshanBBQ]

The idea behidn impulse invariant method is to compute a discrete impulse response, h[n], from the continuous impulse response, h(t), by sampling h(t) every T units of time.
$$h[n] = Th(Tn)$$
The discrete impulse response is the z-transform of this quantity. It's troubling that the problem statement doesn't give you a sampling time. I suppose you will have to keep it symbolic as T.