Time Invariance

A time invariant system is a system that is not affected by time delays or shifts.

Example of System

If $ x(t) = a $, where $ a $ is any real integer and $ t $ are inputs in time, then giving it any time delay $ t_0 $ will not affect its value because the value stays constant all times.

Example of Time Variant System

Given that input is $ t $, in units of time, the system is $ x(t) = t^4 $ which if shifted would change the final output of the system. At a given time $ t = 3 $ seconds, $ t^4 = 81 $. However, if the time is delayed by $ t_0 = 2 $ so that the system is $ x(t-2) = (t-2)^4 $, then $ (t-4)^4 = 16 $.