Definition
A system is called Time Invariant when an input x(t) is sent through a time delay and the system and, regardless of the order in which is goes through, the output is always y(t).
Examples
-Time Invariant-
y(t) = 25x(t)
x(t) -> syst. -> y(t)=25x(t) -> delay -> z(t) = y(t+t0) = 25x(t+t0)
Alternately
x(t) -> delay -> y(t)=x(t+to) -> syst. -> z(t) = 25y(t) = 25x(t+t0)
The outputs are the same=> The system is time invariant
-Non Time Invariant-
y(t) = x(t) + x(2t)
x(t) -> syst. -> y(t) = x(t) + x(2t) -> delay -> z(t) = y(t+t0) = x(t+t0) + x(2t+t0)
Alternately
x(t) -> delay -> y(t) = x(t+t0) -> syst. -> z(t) = y(t) + y(2t) = x(t+t0) + x(2t+2t0)
The outputs are not the same=> The system is not time invariant
