Time Invariance
A system is called "time invariant" if for any input signal x(t) in continuous time or x[n] in discrete time and for any time $ t_0\in{\mathbb R} $ for continuous time or $ n_0\in{\mathbb N} $, The response to the shifted input $ x(t-t_{0}) $ or $ x[n-n_{0}] $ is the shifted output $ y(t-t_{0}) $ or $ y[n-n_{0}] $
$ x(t)\rightarrow system\rightarrow time delay\rightarrow y(t-t_{0}) $
$ x(t)\rightarrow time delay\rightarrow system\rightarrow y(t-t_{0}) $
Time Variant
A system is called "time variant" if for any input signal x(t) in continuous time or x[n] in discrete time and for any time $ t_0\in{\mathbb R} $ for continuous time or $ n_0\in{\mathbb N} $, The response to the shifted input $ x(t-t_{0}) $ or $ x[n-n_{0}] $ is not the shifted output $ y(t-t_{0}) $ or $ y[n-n_{0}] $
$ x(t)\rightarrow system\rightarrow time delay\rightarrow y(t-t_{0}) $
$ x(t)\rightarrow time delay\rightarrow system\rightarrow z(t) $
