# Relation between stability and overshoot?

Is there any relatonship between stability and overshoot? I mean, can we say that a system if it is marginally stable, it will not have overshoot?

• Have you read the relevant Wikipedia page: en.wikipedia.org/wiki/Step_response ? Nov 25, 2019 at 10:36
• Verbal Kint's answer is good, but I think you may need to review the basics of stability first. A system can have some oscillation but be stable (converges to a value). If your system is stable you can still have a decaying oscillation (what overshoot is), or even be metastable and have a continual oscillation that doesn't decay but doesn't diverge to infinity. Once you cover stability, then explore what overshoot is. Nov 25, 2019 at 14:04

This is a complicated subject but one can try to give some guidelines. The below picture shows the typical open-loop gain response of a switching converter: the plant response $$\H(s)\$$ is of 2nd-order while the compensator $$\G(s)\$$ is of 3rd-order. To reduce the order and simplify the analysis, the system is observed in the vicinity of the crossover frequency $$\f_c\$$ and is approximated to a second-order system, without any zero:
What is interesting now is to see how the open-loop phase margin that you select affects the closed-loop quality factor $$\Q\$$. In other words, how can I can select my phase margin to shape the transient response I want. Because this is really the point: you choose the phase margin based on the wanted transient response. If you do the maths as described here, you end up with a simple relationship linking phase margin and quality coefficient: