English: The system is time-invariant (with respect to the signals ${\displaystyle x(t)}$ and ${\displaystyle y(t)}$) if and only if ${\displaystyle y_{2}(t)=y_{1}(t-t_{0})}$ for all time ${\displaystyle t}$ and for any/all real constant ${\displaystyle t_{0}}$ and for any/all input ${\displaystyle x_{1}(t)}$.

For a MIMO system, use:

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