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LinearizingTransformationData[…]

represents data of an AffineStateSpaceModel linearized by functions such as FeedbackLinearize and StateTransformationLinearize using transformation of variables.

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LinearizingTransformationData

LinearizingTransformationData[…]

represents data of an AffineStateSpaceModel linearized by functions such as FeedbackLinearize and StateTransformationLinearize using transformation of variables.

Details

  • A LinearizingTransformationData[…] object ltd can be used to retrieve various properties.
  • The list of available properties is given by ltd["Properties"].
  • Additional information about the properties is listed on function pages FeedbackLinearize, StateTransformationLinearize, and CarlemanLinearize.
  • Typical properties include:
  • "Linearization"type of linearization
    "TransformedSystem"system in the new coordinates
    "InverseStateTransformation"inverse transformation of the state variables

Examples

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Basic Examples  (1)

Feedback linearize a system:

Wolfram Language code: ℱ = FeedbackLinearize[AffineStateSpaceModel[{{Subscript[x, 2] + Subscript[x, 2]^2, Subscript[x, 1]}, {{0}, {1}}, {Subscript[x, 1]}, {{0}}}, {Subscript[x, 1], Subscript[x, 2]}, Automatic, {Automatic}, Automatic, SamplingPeriod -> None]]

Obtain the list of properties:

Wolfram Language code: ℱ["Properties"]

The transformed system:

Wolfram Language code: ℱ["TransformedSystem"]

Scope  (4)

Obtain a particular property value:

Wolfram Language code: 𝒮 = StateTransformationLinearize[AffineStateSpaceModel[{{Subscript[x, 2], Subscript[x, 3], Subscript[x, 4], 0}, {{Subscript[x, 2]/2 - (Subscript[x, 3]*Subscript[x, 4])/ 12}, {Subscript[x, 3]/2}, {Subscript[x, 4]}, {1}}}, {Subscript[x, 1], Subscript[x, 2], Subscript[x, 3], Subscript[x, 4]}, Automatic, {Automatic, Automatic, Automatic, Automatic}, Automatic, SamplingPeriod -> None]]
Wolfram Language code: 𝒮["Linearization"]

Obtain several property values simultaneously:

Wolfram Language code: ℱ = FeedbackLinearize[AffineStateSpaceModel[{{Subscript[x, 2] + Subscript[x, 2]^2, Subscript[x, 1]}, {{0}, {1}}, {Subscript[x, 1]}, {{0}}}, {Subscript[x, 1], Subscript[x, 2]}, Automatic, {Automatic}, Automatic, SamplingPeriod -> None]];
Wolfram Language code: ℱ[{"InverseStateTransformation", "LinearSystem"}]

Some properties could be missing:

Wolfram Language code: ℱ = FeedbackLinearize[AffineStateSpaceModel[{{Subscript[x, 2] + Subscript[x, 2]^2, Subscript[x, 1]}, {{0}, {1}}, {Subscript[x, 1]}, {{0}}}, {Subscript[x, 1], Subscript[x, 2]}, Automatic, {Automatic}, Automatic, SamplingPeriod -> None]];
Wolfram Language code: ℱ["ZeroDynamicsSystem"]

Some properties require multiple arguments:

Wolfram Language code: ℱ = FeedbackLinearize[AffineStateSpaceModel[{{Subscript[x, 2] + Subscript[x, 2]^2, Subscript[x, 1]}, {{0}, {1}}, {Subscript[x, 1]}, {{0}}}, {Subscript[x, 1], Subscript[x, 2]}, Automatic, {Automatic}, Automatic, SamplingPeriod -> None]];

Compute a set of feedback gains based on the linearized system:

Wolfram Language code: κ = StateFeedbackGains[ℱ["LinearSystem"], {-1, -2}];

This can be used to obtain the closed-loop system:

Wolfram Language code: ℱ[{"ClosedLoopSystem", κ}]

Simulate the closed-loop system:

Wolfram Language code: Plot[Evaluate@OutputResponse[{%, {0.1, -1}}, 0, {t, 0, 5}], {t, 0, 5}]
Wolfram Research (2014), LinearizingTransformationData, Wolfram Language function, https://reference.wolfram.com/language/ref/LinearizingTransformationData.html.

Text

Wolfram Research (2014), LinearizingTransformationData, Wolfram Language function, https://reference.wolfram.com/language/ref/LinearizingTransformationData.html.

CMS

Wolfram Language. 2014. "LinearizingTransformationData." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/LinearizingTransformationData.html.

APA

Wolfram Language. (2014). LinearizingTransformationData. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/LinearizingTransformationData.html

BibTeX

@misc{reference.wolfram_2026_linearizingtransformationdata, author="Wolfram Research", title="{LinearizingTransformationData}", year="2014", howpublished="\url{https://reference.wolfram.com/language/ref/LinearizingTransformationData.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_linearizingtransformationdata, organization={Wolfram Research}, title={LinearizingTransformationData}, year={2014}, url={https://reference.wolfram.com/language/ref/LinearizingTransformationData.html}, note=[Accessed: 12-June-2026]}