# Effect of origin poles on stability?

What will be stability if we have only one single pole at origin in s domain?? and what will be the case for multiple poles at origin in s domain?

A system with simple distinct poles on the imaginary axis (and note that the origin is on the imaginary axis) and no poles in the right half-plane is called marginally stable. If you have poles with multiplicity greater than $$1$$ on the imaginary axis, or if there are poles in the right half-plane, then the system is unstable.
• @abtj: It's just as I said, the origin $s=0$ is on the imaginary axis, so a pole at $s=0$ is on the imaginary axis. And, obviously, not all poles on the imaginary axis are necessarily at the origin. – Matt L. Sep 28 '19 at 11:20
• At the risk of stating the obvious, it is not about the number of poles on the unit circle, but about the multiplicity of the poles. Separate simple poles on the unit circle, no matter how many, result in a marginally stable system, poles on the circle with multiplicity greater than $1$ cause the system to be unstable. – Matt L. Sep 29 '19 at 7:35