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:

Scope  (2)

A multi-input, multi-output transfer-function model:

The controllable realization:

The controllable companion realization:

The observable realization:

The observable companion realization:

Controllable and controllable companion realizations are controllable:

Observable and observable companion realizations are observable:

Properties & Relations  (4)

A two-output transfer-function model:

The controllable and controllable companion realizations are controllable:

They are not necessarily observable:

The observable and observable companion realizations are observable:

They are not necessarily controllable:

The controllable and controllable companion realizations are identical for single-input systems:

The observable and observable companion forms are identical for single-output systems:

StateSpaceRealization affects the proper part of an improper transfer function:

The first two states use the specified realization:

Divide the state-space model into the slow and fast subsystems:

The slow subsystem models the strictly proper part of the transfer function:

The fast subsystem models the polynomial part:

Wolfram Research (2010), StateSpaceRealization, Wolfram Language function, https://reference.wolfram.com/language/ref/StateSpaceRealization.html (updated 2012).

Text

Wolfram Research (2010), StateSpaceRealization, Wolfram Language function, https://reference.wolfram.com/language/ref/StateSpaceRealization.html (updated 2012).

BibTeX

@misc{reference.wolfram_2021_statespacerealization, author="Wolfram Research", title="{StateSpaceRealization}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/StateSpaceRealization.html}", note=[Accessed: 28-November-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_statespacerealization, organization={Wolfram Research}, title={StateSpaceRealization}, year={2012}, url={https://reference.wolfram.com/language/ref/StateSpaceRealization.html}, note=[Accessed: 28-November-2021 ]}

CMS

Wolfram Language. 2010. "StateSpaceRealization." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/StateSpaceRealization.html.

APA

Wolfram Language. (2010). StateSpaceRealization. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/StateSpaceRealization.html