Abstract
This chapter introduces the transfer function as a Laplace-domain operator, which characterizes the properties of a given dynamic system and connects the input to the output. The transfer function for single-input, single-output (SISO) systems and transfer function matrix for multiple-input, multiple-output (MIMO) systems can be used to determine the forced time response and the free time response with nonzero initial conditions. The complex impedance is introduced as a transfer function at the element level, which enables deriving the transfer function of dynamic systems directly in the Laplace domain. The transfer function can be utilized to study the stability of dynamic systems. MATLAB and Simulink examples illustrating the use of transfer function by means of built-in capabilities are incorporated alongside many solved examples that use the standard transfer function formulation and solution.
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