"In control systems, an open loop transfer function having poles in left half plane, should have positive phase margin and positive gain margin to ensure closed loop stability."
I was trying to interpret this statement. I was able to figure out why is the statement correct for gsin margin. I did so by relating root locus and Nyquist plots as follows:
For root locus with open loop poles on left half plane, we get a stable closed loop system untill the locus crosses jw axis. This may happen for larger values of gain, K. So the system is stable for smaller values of gain K. This reflects that the Nyquist plot must have smaller K, and hence would pass the negative real axis at some place greater than -1 (analogous to jw axis.) This would ensure a positive phase margin.
I made many failed attempts to prove similarly for the positive phase margin, too. But I could not figure out why the phase margin is positive for a stable closed loop system (for a open loop function with left hand poles.)