How to deal with a negative pole (unstable) in the pre-filter of a control system? So while answering how to design a PI controller for a first order time delayed system   (Question Here ) 

Here is the closed loop equation to a control system:

$$
G_C(s) = \frac{\frac{K}{T}(1-sT)(s)} { s^3 + (\frac{1}{T} + a - KK_p)s^2 + (\frac{a}{T} + \frac{KK_P}{T} +K_I)s+\frac{KK_I}{T}} 
$$ 

Question: How do you deal with normalizing the numerator in your closed loop transfer function when the filter is unstable? (Pole on RH of plane) 

Typically you introduce a filter before your controller that does:

$$ \frac{1} {\frac{K}{T} (1-sT)(s)} $$

to normalize the numerator 

But the filter itself is unstable because of the term:

$$ \frac{1}{(1-sT)}$$ is unstable for a step response which would create an issue realizing the system at all. 

One way I've thought about dealing with this is multiplying it by its complex conjugate 
$$
\frac{(1+sT)} {(1+sT)}$$

but im not really sure about the merits of it.
In general, in order to stabilise a system, however complex, if you have the transfer function $G(s)$, you introduce a feedback loop with a new function $F(s)$.

Write the closed loop transfer function for the new system with the added $F(s)$, and then find $F(s)$ in order for the new system to be stable. This is like the first exercise in any control book in order to offer an example of stabilising a system via negative Feedback.

Check the book from Ogata on control engineering for reference.