Why Is Transfer Function Defined for Linear Systems Only?

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Transfer functions are defined exclusively for linear systems because they represent the output-to-input signal ratio, which can only be accurately established when both signals share the same form. This relationship is crucial, as nonlinear systems do not maintain proportionality between input and output. Additionally, transfer functions are typically defined under the assumption of zero initial conditions to simplify analysis and ensure consistency in system behavior. Defining them with initial conditions complicates the relationship and can lead to inaccuracies. Therefore, the linearity and zero initial condition assumptions are fundamental to the applicability of transfer functions in control systems.
srinaath
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i have few queries regarding control system in electrical engineering...
1)transfer function is defined for linear system ? why is that so...
2)why transfer function is defined with zero initial condition...why not with initial condition
 
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A transfer function is the output-to-input signal ratio. Such a ratio can be defined for equal signals forms only.
(Can you divide a triangle form by a sinus signal?).
The output signal form is equal to the form of the input signal for linear systems only.
 
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