I have this open loop transfer function and I have to study the stability of the closed loop transfer function using the Nyquist criterion. What I got is that the characteristic equation 1+GH(s)=0 has two roots inside the Nyquist contour, the GH(s) transfer function has zero poles in the right hand plane and that the number of loops around -1 in the Nyquist Diagram is 2 so according to the Nyquist criterion, Z=N+P in which I get 2=2. So the system is stable, however the response I get to an impulse is this:
Review the Wikipedia article, or your textbook.
The number of times the plot can loop around the critical point (-1 for open-loop plots, 0 for closed-loop) is equal to the number of unstable poles minus the number of unstable zeros. This is because you are counting the number of poles minus the number of zeros that are encircled by traveling up the \$j\omega\$ axis, then around the entire right-half plane.
So your Nyquist plot is actually predicting an unstable system, which is exactly what you have.