DualSystemsModel

DualSystemsModel[ssm]

gives the dual of the state-space model ssm.

Details

  • The state-space model ssm can be a standard or descriptor StateSpaceModel.
  • The original and dual systems for a standard StateSpaceModel[{a,b,c,d}]:
  • The original and dual systems for a descriptor StateSpaceModel[{a,b,c,d,e}]:

Examples

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Basic Examples  (1)

The dual of a system:

Scope  (3)

A dual model:

All variables are considered as complex:

Simplify, assuming all variables are real:

Specify only some variables to be real:

The dual of a descriptor system:

Properties & Relations  (4)

The controllable and observable realizations have a dual relationship:

A similar relationship exists between the controllable companion and observable companion forms:

An uncontrollable but observable model:

The dual model is controllable but not observable:

The controllability matrix of a system is the conjugate transpose of the observability matrix of the dual system and vice versa:

The estimator gains are the conjugate transpose of feedback gains of the dual model and vice versa:

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

Text

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

BibTeX

@misc{reference.wolfram_2021_dualsystemsmodel, author="Wolfram Research", title="{DualSystemsModel}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/DualSystemsModel.html}", note=[Accessed: 21-September-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_dualsystemsmodel, organization={Wolfram Research}, title={DualSystemsModel}, year={2012}, url={https://reference.wolfram.com/language/ref/DualSystemsModel.html}, note=[Accessed: 21-September-2021 ]}

CMS

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

APA

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