Frequency Response
Frequency response is related to the steady-state response of a linear system when a harmonic function is applied as the input.
The steady-state response is the linear system's output after the transient response has decayed to zero.
The requirement that the transient response should have decayed to zero after some time calls for the system to be stable.
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Definition of a Linear System
Consider a plant with one input and one output. Suppose you run the system for a period of time while recording the input and output signals. Call the input signal u1(t) and the output signal y1(t).
Perform this experiment again with a different input signal. Name the input and output signals from this run u2(t) and y2(t), respectively.
Now perform a third run of the experiment with
the input signal u3(t) = u1(t) + u2(t).
The plant is linear if the output signal y3(t)
is equal to the sum y1(t) +y2(t) for any arbitrarily
selected input signals u1(t) and u2(t).
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