Electrical Engineering ⇒ Topic : Linear and Non-linear Systems
Linear and Non-linear Systems
If a system satisfies the property of homogeneity and the property of superposition, the system is said to be linear.
Let the system produces output y(t) for an input x(t). If the input is scaled 'a' times, the output will also be scaled by 'a' times for all values of 'a' and x(t). Therefore, we can write mathematically as follows:
x(t) → y(t)
ax(t) → ay(t)
If two inputs x1(t) and x2(t) are applied to a system simultaneously, the overall output will be the combined effects of x1(t) and x2(t).
x1(t) + x2(t) → y1(t) + y2(t)
Combining these properties, we can write the following for a linear system:
If x1(t) → y1(t) and x2(t) → y2(t), then
a1x1(t) + a2x2(t) → a1y1(t) + a2y2(t)
If any system does not satisfy the above two conditions, the system is called non-linear. Usually,non-linearity arises in a physical system due to non-linear input and output relation of its components.
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