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.
Examples
Examples
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$1$, for $\dot{x} = f(x) = 1 - x$
High school
$1$ is the steady state of $\dot{x} = 1 - x$, because every solution settles there.
Properties
- For a stable linear time-invariant system with transfer function $G(s)$, the steady-state response to $\sin(\omega t)$ is $\abs{G(i \omega)} \sin(\omega t + \angle G(i \omega))$.