Page "Control theory" Paragraph 68

When the appropriate conditions above are satisfied a system is said to be asymptotically stable: the variables of an asymptotically stable control system always decrease from their initial value and do not show permanent oscillations.

Permanent oscillations occur when a pole has a real part exactly equal to zero ( in the continuous time case ) or a modulus equal to one ( in the discrete time case ).

If a simply stable system response neither decays nor grows over time, and has no oscillations, it is marginally stable: in this case the system transfer function has non-repeated poles at complex plane origin ( i. e. their real and complex component is zero in the continuous time case ).

Oscillations are present when poles with real part equal to zero have an imaginary part not equal to zero.