# Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# ToContinuousTimeModel

ToContinuousTimeModel[lsys]
gives the continuous-time approximation of the discrete-time systems models lsys.

ToContinuousTimeModel[tfm,s]
specifies the transform variable s.

## Details and OptionsDetails and Options

• ToContinuousTimeModel is also known as inverse sampling.
• The systems model lsys can be a TransferFunctionModel or StateSpaceModel.
• ToContinuousTimeModel accepts a Method option that can be used to specify the approximation method.
• Possible settings for the Method option include:
•  "ForwardRectangularRule" Euler forward method "BackwardRectangularRule" Euler backward method "BilinearTransform" Tustin bilinear approximation "ZeroPoleMapping" exact matching of zeros and poles "ZeroOrderHold" piecewise constant approximation "FirstOrderHold" piecewise linear (triangular) approximation
• The default setting implements the bilinear transformation.
• The setting Method->"ZeroPoleMapping" does not support time delays.
• A bilinear transform with critical frequency ω radians per time unit can be specified by setting Method->{"BilinearTransform","CriticalFrequency"->ω}.
• The method gives the non-causal first-order hold equivalent.
• When approximating TransferFunctionModel objects, can be specified as a suboption.
• The setting Method->{m,"StateSpaceConversion"->True} computes the approximation using the state-space representation and converts the result to the transfer-function representation.
• The setting "StateSpaceConversion"->False computes using the transfer-function object.
• The setting "StateSpaceConversion"->Automatic computes the approximation using the transfer-function representation, except for the method.

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

A continuous-time approximation of a discrete-time system:

 In[1]:=
 Out[1]=