Steady state
High school
The steady state of a system is the behavior it settles into after its initial transients die out. A steady state can a constant value or a steady oscillation.
Undergraduate
The steady-state response of a stable system to an input is what remains of its response as $t \to \infty$, after the transient response (which depends on the initial state) decays.
Properties
- For a stable linear time-invariant system with transfer function $G(s)$, the steady-state response to $\sin(\omega t)$ is $\lvert G(i \omega) \rvert \sin(\omega t + \angle G(i \omega))$.