English: The system satisfies the superposition principle (with respect to the signals ${\displaystyle x(t)}$ and ${\displaystyle y(t)}$) if and only if ${\displaystyle y_{3}(t)=a\,y_{1}(t)+b\,y_{2}(t)}$ for all time ${\displaystyle t}$ and for any real constants ${\displaystyle a}$ and ${\displaystyle b}$ and for any inputs ${\displaystyle x_{1}(t)}$ and ${\displaystyle x_{2}(t)}$. This is exactly equivalent to satisfying both the homogeneity and additivity properties for the same conditions.

For a MIMO system, use:

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