The following picture shows Nyquist Plot according to optimal control LQR. Nyquist Plot for LQR
It shows regions that when avoided, it guarantees gain margin $GM = \infty$, phase margin $PM = 60°$ (at least). I need a little bit of clarification of how that is proved when the following regions are avoided. I understand the following:
1) The point $z=-1 + 0j$ (center of the shaded circle), is the point where gain $|G(j\omega)| = 1$, and phase $ \varphi= 180°$ . When this point is reached, the negative feedback becomes positive (because of the phase change), resulting in disaster.
2) Allegedly, the following graph proves that gain is infinite, but it seems false because I can reach phase $\varphi = -180°$, that is for gain lower than $-2 + 0j$