Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.View current documentation (Version 11.2)

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:

In[1]:=
Click for copyable input
Out[1]=

Add an identity matrix to create a descriptor form:

In[1]:=
Click for copyable input
Out[1]=

Obtain the descriptor StateSpaceModel:

In[1]:=
Click for copyable input
Out[1]=

By default, the standard form is obtained:

In[2]:=
Click for copyable input
Out[2]=

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

In[1]:=
Click for copyable input
Out[1]=

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

In[2]:=
Click for copyable input
Out[2]=

Obtain the result from StateSpaceTransform in the descriptor form:

In[1]:=
Click for copyable input
Out[1]=

By default, the form is unaltered:

In[2]:=
Click for copyable input
Out[2]=
Introduced in 2012
(9.0)
| Updated in 2014
(10.0)