A stable feedback system can still fail to track a reference exactly after its transient has disappeared.

For unity feedback,

$$E(s)=\frac{R(s)}{1+L(s)},$$

where $L(s)$ is the loop transfer function.

When the final value theorem applies, the steady-state error is

$$e_{ss}=\lim_{t\to\infty}e(t)=\lim_{s\to0}sE(s).$$

The low-frequency behavior of $L(s)$ therefore determines long-term tracking.

The system type is the number of poles at the origin in the loop transfer function. Each integrator increases the class of polynomial reference signals that can be tracked with finite or zero steady-state error.

For example, a type-0 loop generally has a nonzero error to a step reference, while a type-1 loop can have zero step error but a finite error to a ramp.

Steady-state accuracy is therefore a low-frequency property of the complete loop, not simply a property of the plant or controller considered alone.