# What does asymptotic stability mean ? and can a system have lower than 90deg of phase margin and still be stable?

why bode stability criteria dictates 90deg of phase margin ? my understanding is that it is so when a system is cascaded with another there's a margin so the phase doesn't get to 180 and over, am i right ?

Cascading stages isn't a problem - it's a problem when you apply "negative" feedback from the output of the last stage to the input of the first stage. That's when trouble can start.

So, if both stages shift by 90 degrees at a certain frequency then applying negative feedback is really applying positive feedback.

Simple words: -

• Asymptotic stability - after returning the input to a control system to the neutral value, the output falls back to zero.
• Marginal stability (as per an integrator) - after returning the input to the neutral value, the output does not fall back to zero.
• Andy aka, what means "removing"? Open circuit at the input? Shouldn`t it mean: Shorting the input to zero volts? According to your "definition" an integrator circuit would be not absolutely stable - which is wrong. An integrator is stable! – LvW Apr 27 '18 at 15:40
• @LvW yes I'll fix the ambiguity of the word removal. – Andy aka Apr 27 '18 at 16:32

It is not true that "bode stability criteria dictates 90deg of phase margin". A system with feedback is classified as "asymptotic stable" even in case of a phase margin of 10 deg (or lower).
In most cases, a margin in the region of 60 deg is envisaged because, in this case, the step response shows only a slight overshoot.