Assume that you have the feedback control system shown below.  In this system you are using proportional control, and you have a gain, K_p, that you can adjust.  (If you are using integral control, or something else, you can still put it into this framework.)

If you have a Nyquist plot for the system system being controlled (G(s)), then you can determine the gain at which the system becomes unstable.

        Here is a Nyquist plot for a typical system.

• The arrows on the plot indicate the direction of increasing frequency.
• The solid plot is for positive frequencies, and the dotted plot is for negative frequencies.
• The plot starts at zero frequency at a gain of about 0.4
• The plot intersects the negative real axis at about -0.62

• Determine the intersection with the negative real axis.
• The value here is -0.62.
• Determine the factor by which the plot can be resized so that it would go through -1.
• Here you would be able to increase the plot size by a factor of 1/0.62 = 1.61.
• The resizing factor is the largest gain that you can have.
• The largest gain you can have for this system is K_p = 1.61.