A linear system is one in which the relationship between input and output is linear.
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 + βu2) = aT(u1) + βT(u2)
where a and β are constant.
