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}]:
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- The original and dual systems for a descriptor StateSpaceModel[{a,b,c,d,e}]:
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Examples
open all close allScope (3)
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:
Text
Wolfram Research (2010), DualSystemsModel, Wolfram Language function, https://reference.wolfram.com/language/ref/DualSystemsModel.html (updated 2012).
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