Which transfer function represents a stable system

The stability of a linear closed-loop system can be determined from the locations of closed-loop poles in the s-plane.

Stable System:

If all the roots of the characteristic equation lie on the left half of the 's' plane, i.e. if all the roots have negative real parts, then the system is said to be a stable system.

Ex: For a system with Closed Loop Transfer function as:

\(C.L.T.F.=\frac{1}{s+4}\)

It has a pole at s = - 4. The pole has a negative real part. This makes the system absolutely integrable and therefore, stable.

Analysis:

Since for all the systems, we can see that the poles are not on right half of the s-plane. Hence all the system is stable.