Definition
If the cascade $ x(t) \to timedelay \to sys \to z(t) $ yields the same output as the cascade $ x(t) \to sys \to timedelay \to z(t) $ for any $ t_{0} $, then the system is called "time invariant".
Example of Time-Invariant System
Example of Non-Time-Invariant System
Equations: $ y(t) = 3x(t) $ and $ x(t) = 3t $
$ x(t) \to timedelay \to sys \to z(t)=3(3t-t_{0}) $
$ x(t) \to sys \to timedelay \to z(t)=9t-t_{0} $
Since $ 3(3t-t_{0}) $ does not equal $ 9t-t_{0} $, the system is not time-invariant.
