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Hometime invariant

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# time invariant

A dynamical system is time-invariant if its generating formula is dependent on state only, and independent of time. A synonym for time-invariant is autonomous. The complement of time-invariant is time-varying (or nonautonomous).

For example, the continuous-time system $\dot{x}=f(x,t)$ is time-invariant if and only if $f(x,t_{1})\equiv f(x,t_{2})$ for all valid states $x$ and times $t_{1}$ and $t_{2}$. Thus $\dot{x}=\sin x$ is time-invariant, while $\dot{x}=\frac{\sin x}{1+t}$ is time-varying.

Defines:

time-invariant, shift-invariant

Related:

AutonomousSystem

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

00A05*no label found*

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