DescriptorStateSpace

DescriptorStateSpace

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

Details

  • 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 a standard representation cannot be obtained, and StateSpaceTransform does not alter the representation.

Examples

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Basic Examples  (7)

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

Add an identity matrix to create a descriptor form:

Obtain the descriptor StateSpaceModel:

By default, the standard form is obtained:

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

This is because it is not possible to obtain the standard form:

When possible, the standard form is obtained:

The descriptor form:

In some cases, the standard form can have fewer states:

However, the order of the system is the same in both cases:

Obtain the result from StateSpaceTransform in the descriptor form:

By default, the form is unaltered:

Scope  (6)

Create a standard state-space model from a descriptor state-space model:

Create a descriptor state-space model from a standard state-space model:

Convert a proper transfer-function model to a descriptor state-space model:

Create a descriptor state-space model from an ODE:

Obtain the state transformation of a standard StateSpaceModel in descriptor form:

It gives the same result as an explicit descriptor specification:

Similar results can be obtained with the inverse transformation as well:

A descriptor StateSpaceModel with an invertible descriptor matrix:

Its state transformation can be obtained in standard form:

Properties & Relations  (2)

Improper transfer-function models will create descriptor state-space models by default:

There is no standard state-space realization:

A descriptor StateSpaceModel with a noninvertible descriptor matrix:

StateSpaceTransform produces a descriptor model:

The state transformation cannot be obtained in standard form:

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