step response

The system G(s) = (s+1)/( s*(s+3)*(s*s+4*s+8)) with poles at
0
-3.0000
-2.0000 + 2.0000i
-2.0000 - 2.0000i
and a zero at -1 has all stable poles, i.e. in the left hand of the s-plane . However the step response of the system is unstable !!!!

This is most probably due to the pole at the origin. The system then behaves as a double integrator. The impulse response of the plant does not decay to zero ! The plant is decidedly unstable.

This is food for thought , since before this I thought that the stability of the system could be determined my the location of poles alone. It now seems that its also important that whether the poles in question are open loop or closed loop !