Negative feedback - equilibrium

I have a basic question regarding negative feedback and stability. As I've understood it, negative feedback is supposed to promote equilibrium.

But suppose we have negative feedback loop block diagram, with open loop gain A, and feedback $\beta$. Both positive greater than 0.

$Output = \dfrac{A}{1+\beta\ A} * Input$

Now suppose there's an instability at the output... say the output is higher than the above value by $\Delta$.

Won't this instability grow at the output until some rail voltage is hit. ie: the instability becomes: $\Delta (-\beta A)^n$ , where n is the number of iterations through the loop.

If $\beta A$ is greater than 1, won't this instability keep growing till some rail voltage is hit.

Is there something wrong with my above analysis? how is equilibrium reached? Thanks.

• What do you mean by 'an instability at the output'? If the output increases by $\small\Delta$, the error becomes $\small -\Delta$, and hence the output reduces until the error is again zero. That's negative feedback. – Chu Mar 1 '16 at 13:48