I am reviewing bode plots and s-plane (pole-zero plots). I seem to have some confusion about them and how they relate to each other. I believe one is for closed-loop systems, the other is for open-loop.
My question is : If I have a first order, single pole system and the pole lies on the imaginary axis. From what I know about the s-plane, this would make it an unstable system.
If I plot the bode plot, I will see an unbounded peak at the pole frequency in the magnitude plot.
However, the phase shift will be a maximum of -90 degrees - nowhere close to the -180 which is required for instability. How does this make sense? The bode plot is still indicating the system is stable???