T1 =

-67.34 s + 1.563e06


0.0008762 s^2 + 0.09793 s + 2273

T2 =

2.447e07 s^2 + 7.695e11 s + 2.687e13


2.483e-05 s^4 + 77.99 s^3 + 1364 s^2 + 3.142e06 s

Screen shots of Bode plots for the above transfer functions are attached with respective file names. Yes, I was taught in control system course that both the Gain Margin (GM) and Phase Margin (PM) should be positive for a stable system, but the bode plot of T2 shows that the system is stable even with negative GM. Therefore, I intrepreted this as the system is unstable only when its phase is equal to ± 180 ° at its open loop gain of unity. Because, only at this condition the closed loop gain becomes infinity.

However, my interpretation goes wrong with the system function T1, where both GM and Phase Margine (PM) are negative but its phase is not equal to ± 180 ° at its open loop gain of unity.

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