({{, (RefLink[LinearizingTransformationData, paclet:ref/LinearizingTransformationData])[…] 
represents data of an (RefLink[AffineStateSpaceModel, paclet:ref/AffineStateSpaceModel]) linearized by functions such as (RefLink[FeedbackLinearize, paclet:ref/FeedbackLinearize]) and (RefLink[StateTransformationLinearize, paclet:ref/StateTransformationLinearize]) using transformation of variables.}})

OpenersNotesSection(Spacer1)Details

A (RefLink[LinearizingTransformationData, paclet:ref/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 (RefLink[FeedbackLinearize, paclet:ref/FeedbackLinearize]), (RefLink[StateTransformationLinearize, paclet:ref/StateTransformationLinearize]), and (RefLink[CarlemanLinearize, paclet:ref/CarlemanLinearize]).

Typical properties include:

OpenersPrimaryExamplesSection(Spacer1)Examples  (5)

OpenersExampleSection0(Spacer1)Basic Examples  (1)

Feedback linearize a system:

ℱ=FeedbackLinearize[(AffineStateSpaceModelFull[(Subscript[x, 2])+(Subscript[x, 2]^2), (Subscript[x, 1]), 0, 1, (Subscript[x, 1]), 0, (Subscript[x, 1]), (Subscript[x, 2]), \[Null], \[Null], AutomaticAutomatic, ])]

Obtain the list of properties:

ℱ["Properties"]

The transformed system:

ℱ["TransformedSystem"]

OpenersExampleSection1(Spacer1)Scope  (4)

Obtain a particular property value:

𝒮=StateTransformationLinearize[(AffineStateSpaceModelFull[(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]), \[Null], \[Null], \[Null], \[Null], \[Null], AutomaticAutomatic, ])]

𝒮["Linearization"]

Obtain several property values simultaneously:

ℱ=FeedbackLinearize[(AffineStateSpaceModelFull[(Subscript[x, 2])+(Subscript[x, 2]^2), (Subscript[x, 1]), 0, 1, (Subscript[x, 1]), 0, (Subscript[x, 1]), (Subscript[x, 2]), \[Null], \[Null], AutomaticAutomatic, ])];

ℱ[{"InverseStateTransformation","LinearSystem"}]

Some properties could be missing:

ℱ=FeedbackLinearize[(AffineStateSpaceModelFull[(Subscript[x, 2])+(Subscript[x, 2]^2), (Subscript[x, 1]), 0, 1, (Subscript[x, 1]), 0, (Subscript[x, 1]), (Subscript[x, 2]), \[Null], \[Null], AutomaticAutomatic, ])];

ℱ["ZeroDynamicsSystem"]

Some properties require multiple arguments:

ℱ=FeedbackLinearize[(AffineStateSpaceModelFull[(Subscript[x, 2])+(Subscript[x, 2]^2), (Subscript[x, 1]), 0, 1, (Subscript[x, 1]), 0, (Subscript[x, 1]), (Subscript[x, 2]), \[Null], \[Null], AutomaticAutomatic, ])];

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

κ=StateFeedbackGains[ℱ["LinearSystem"],{-1,-2}];

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

ℱ[{"ClosedLoopSystem",κ}]

Simulate the closed-loop system:

Plot[Evaluate@OutputResponse[{%,{0.1,-1}},0,{t,0,5}],{t,0,5}]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[FeedbackLinearize, paclet:ref/FeedbackLinearize])  ▪  (RefLink[StateTransformationLinearize, paclet:ref/StateTransformationLinearize])  ▪  (RefLink[CarlemanLinearize, paclet:ref/CarlemanLinearize])  ▪  (RefLink[AffineStateSpaceModel, paclet:ref/AffineStateSpaceModel])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Nonlinear Control Systems, paclet:guide/NonlinearControlSystems])}})}})