Wolfram Language & System 12.0 (2019)|Legacy Documentation

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TransferFunctionModel

represents the model of the transfer-function matrix m with complex variable s.

specifies the numerator num and denominator den of a transfer-function model.

specifies the zeros z, poles p, and gain g of a transfer-function model.

gives the transfer-function model of the systems model sys.

TransferFunctionModel can represent scalar and multivariate systems in continuous or discrete time.
Time delays can be included in any transfer-function model, by using SystemsModelDelay.
In TransferFunctionModel[{num,den},s], num must be a matrix, and den can be specified as a matrix or just the common denominator.
TransferFunctionModel does not cancel any pole or zero of the matrix elements.
In TransferFunctionModel[sys], the following systems can be converted:
AffineStateSpaceModel approximate Taylor conversion

NonlinearStateSpaceModel approximate Taylor conversion

StateSpaceModel exact conversion
The following options can be given:

Method	Automatic	the method to obtain the transfer function of a state-space model
SamplingPeriod	Automatic	the sampling period of the system
SystemsModelLabels	Automatic	labels for the input and output variables

Settings for the Method option include "DeterminantExpansion", "ResolventIdentities", "Inverse", and "Generic". With a setting Method->Automatic, the transfer-function model is computed using determinant expansion.