Let x(t) and y(t) with F.T. x(f) and y(f) respectively be related as shown in figure

Then y(f) is

Numerator power will higher than denominator, and such transfer functions is not realizable.

All linear system possess the property of superposition i.e., if input u₁ gives output y₁ and input u₂ gives output y₂ then input u₁ + u₂ will give output y₁ + y₂.

Superposition implies homogencity i.e., if input u gives output y, then input ku gives output ky where k is a rational number.

In general a system is linear if a transformation T satisfies the relation

T(au₁ + ?u₂) = aT(u₁) + ?T(u₂)

where a and ? are constant.