Consider a unit feedback system $$ X(s) = \frac{G(s)}{1+G(s)} $$
where the open loop transfer function of the system is $$ G(s) = \frac{s-1}{s(s+1)} $$
Open loop Bode & Nyquist plots: http://www.wolframalpha.com/input/?i=nyquist+plot+%28s-1%29%2F%28s%28s%2B1%29%29
It's easy to see from the Bode plot that the system is stable (phase does not cross $ 180^\circ $).
According to the textbook I'm using (Modern Control Systems, Dorf, 12th ed), the system is stable iff no poles of $ X(s) $ are on the right half s-plane. However this case seems to be a contradiction, because $$ X(s) = \frac{s-1}{s^2+2s-1} $$ has a pole $ -1+\sqrt{2} $, which is located on the right half s-plane.
Could anyone please point out what/where I missed?
Your open loop gain will be one at a frequency of one radian/sec. At this frequency you will have phase shift of 90 degrees from the pole at zero, 45 degrees from the left half plane pole, and another 45 degrees from the right half plane zero. Total of 180 degrees.