StateSpaceRealization

StateSpaceRealization

is an option to StateSpaceModel that specifies its canonical representation.

Details

  • The following settings can be used:
  • Automaticautomatically determine realization
    "Controllable"the controllable realization
    "ControllableCompanion"the controllable companion realization
    "Observable"the observable realization
    "ObservableCompanion"the observable companion realization
  • The controllable form is obtained by computing the controllable companion form of the subsystems corresponding to each input and combining the results.
  • For the proper transfer-function matrix , the controllable companion form is
  • The identity matrix has dimension .
  • The observable form is obtained by computing the observable companion form of the subsystems corresponding to each output and combining the results.
  • For the proper transfer-function matrix , the observable companion form is
  • The realizations are similar for discrete-time systems.
  • For the improper transfer-function , the polynomial part is realized using descriptor variables, and the proper rational part is realized using the specified form. »
  • StateSpaceModel[tfm,StateSpaceRealization->Automatic] gives the controllable realization of the transfer-function model tfm.

Examples

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Basic Examples  (1)

Controllable and observable realizations of a SISO system:

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In[2]:=
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Out[2]=
In[3]:=
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Out[3]=

Scope  (2)

Properties & Relations  (4)

See Also

JordanModelDecomposition  ControllableDecomposition  ObservableDecomposition

Introduced in 2010
(8.0)
| Updated in 2012
(9.0)