# Infinite Phase Margin

I have been assigned a control systems problem, where I am supposed to stabilize a system using a controller technique from the frequency domain. When I implemented the system on Matlab and calculated the phase margin of the system it turned out to be infinite. I am not exactly sure what that means.

Can someone tell me what exactly does it mean that the phase margin comes out infinite, and how can such a system be stabilised?

This is my code:

clc
clear all
close all
num=[1];
den=[1 0 -9];
sys=tf(num,den);
bode(sys);
[Gm,Pm,wcp,wcg]=margin(num,den)


• What is the step response of the open loop system? Is the open loop system unstable? Does it have right hand plane poles? If yes, you have to use the full Nyquist criterion. Don't just look at the phase margin. It is misleading. – AJN Dec 31 '20 at 1:21

Your system $$\\frac{1}{s^2 - 9}\$$ has gain less than 0 dB at all frequencies. The bode plot you have plotted shows that clearly. Since the gain doesn't cross 0 dB anywhere, the phase margin is not well defined.
Apart from the above, this system is open loop unstable. The open loop system sys has a pole at $$\s = +3\$$. For systems which are open loop unstable like this system, use the full Nyquist criterion (counting the encirclements) to determine stability.