Suppose we have two third order systems (a and b), with three poles and two zeroes,poles for both the systems are at the same positions in frequency domain but these systems differ in the placement of their zeroes as shown in the figure below:
The abovve figure is a plot of the loop gain of the systems. Here za1 and za2 are the zeroes for system a and zb1 and zb2 for system b. The exact shape of the magnitude plot of loop gain would differ for the two plots, I only intend to highlight the position of zeroes for the two systems.
In system a the zeroes lie before the unity loop gain frequency whereas in system b they lie after the unity loop gain frequency. Suppose unity gain frequency lies away from the zeroes of both the systems. Clearly the phase margin in case a is close to 90deg while that in case b is close to 270deg. Thus we would conclude that system b is unstable.
My question is, since the stability depends only on the system poles which are same in both the cases, how do these systems differ in their stability?