DescriptorStateSpace

DescriptorStateSpace
is an option to StateSpaceModel and StateSpaceTransform that specifies whether to use descriptor or standard representation.

DetailsDetails

  • In StateSpaceModel[{a,b,c,d,e}], the matrix e is the descriptor matrix.
  • The equations governing continuous-time standard and descriptor state-space models are:
  • standard state space
    descriptor state space
  • Discrete-time systems have analogous forms.
  • The option can take the following values:
  • Automaticautomatically determine the representation
    Falseuse standard state-space representation
    Trueuse descriptor state-space representation
  • With the setting DescriptorStateSpace->Automatic, StateSpaceModel uses the descriptor representation only if e is singular, and StateSpaceTransform does not alter the representation.

ExamplesExamplesopen allclose all

Basic Examples  (5)Basic Examples  (5)

Invert the descriptor matrix to create a standard state-space model:

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Add an identity matrix to create a descriptor form:

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Obtain the descriptor StateSpaceModel:

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By default, the standard form is obtained:

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For singular systems, the descriptor form is obtained by default:

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Because the descriptor matrix is singular, it is not possible to obtain the standard form:

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Obtain the result from StateSpaceTransform in the descriptor form:

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By default, the form is unaltered:

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Introduced in 2012
(9.0)
| Updated in 2014
(10.0)