Consider a hypothetical system with open-loop transfer function $G(s)$.  

Place it in *positive* feedback with unit gain. (That is, take its output and directly *add* it to its input.)  

The closed-loop system now satisfies $Y(s) = G(s) (X(s) + Y(s))$, i.e.:
$$\frac{Y(s)}{X(s)} = \frac{G(s)}{1 - G(s)}$$

This is, of course, simply Black's formula.

### My questions:

If we have $G(s) = 2$, then this system stable? Why?

Intuitively, this system is (obviously!) unstable, because it is in positive unit feedback with gain > 1.  

Yet according to Black's formula, it is actually a *stable* system with gain $2 / (1-2) = -2$!  

(Notice that it has no poles in the right half-plane -- in fact, it has no poles or zeros at all!)

What is there a discrepancy between the math and my intuition? Which one is correct and why?  

What assumptions am I breaking exactly, if any?