Linear system

In mathematics and systems theory, a linear system is one that can be described with linear mappings alone. Most systems found in nature don't have this property, they are called non-linear.

Linear System Media

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  Block diagram illustrating the additivity property for a deterministic continuous-time SISO system. The system satisfies the additivity property or is additive if and only if y_3(t) = y_1(t) + y_2(t) for all time t and for all inputs x_1(t) and x_2(t). Click image to expand it.

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  Block diagram illustrating the homogeneity property for a deterministic continuous-time SISO system. The system satisfies the homogeneity property or is homogeneous if and only if y_2(t) = a \, y_1(t) for all time t, for all real constant a and for all input x_1(t). Click image to expand it.

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  Block diagram illustrating the superposition principle for a deterministic continuous-time SISO system. The system satisfies the superposition principle and is thus linear if and only if y_3(t) = a_1 \, y_1(t) + a_2 \, y_2(t) for all time t, for all real constants a_1 and a_2 and for all inputs x_1(t) and x_2(t). Click image to expand it.