# Why is this second order system difficult to control?

Why is system of the type

$$T = 1/(s^2 - 1)$$ Difficult to control using standard control methods?

When I look at frequency plots, it doesn't seem to give me any important information as to why this system would be difficult to control using classical methods

Can someone who knows control theory (especially the part about compensators or other classical control techniques) inform me as to why this system would be difficult to be controlled using classical frequency based methods?

$\dfrac{1}{(s^2-1)}$ factorises to $\dfrac{1}{(s+1)(s-1)}$, which has a stable pole at $s=-1$ and an unstable pole at $s=1$.
If this is the open-loop TF (you don't say if you wish to close the loop around this TF), then it can be stabilised by placing a zero at $s=-a$, giving an OLTF:$\dfrac{s+a}{(s^2-1)}$, and a CLTF: $\dfrac{s+a}{s^2-1+s+a}=\dfrac{s+a}{s^2+s+(a-1)}$, which is stable for $a>1$.