# Bode plot gives negative stability margins for a stable plant

I have a plant whose transfer function has all the poles in the left half of the s-plane (obtained the poles using Wolfram Alpha). However, its bode plot gives negative phase and gain margins; I obtained the bode plot from both MATLAB and Wolfram Alpha and they agree with each other. I am not able to get around this fact. How is this possible? My characteristic polynomial is  • Matlab's site has some information on when you have multiple 0dB crossings (which is the case here): mathworks.com/help/control/ug/… Nov 8, 2019 at 16:18
• @jDAQ But this is the plot just for the open loop system (plant itself), not the closed loop. Then how do we relate this to closed loop being unstable? And could you please explain why the reason you gave (involving gain and phase) holds? Nov 8, 2019 at 18:01
• I retract my previous comments, I reread cds.caltech.edu/~murray/books/AM08/pdf/… and the stability margin is just a way to evaluate for how much more gain or phase delay the system will remain (if it was at all) stable. And the author show some examples that that can also be a very poor metric to it, since it does not account for both a change in gain and phase.
– jDAQ
Nov 9, 2019 at 5:24