StateTransformationLinearize

StateTransformationLinearize[asys]
linearizes the AffineStateSpaceModel asys by state transformation.

StateTransformationLinearize[asys,{z,lform}]
specifies the new states z and form of linearization lform.

StateTransformationLinearize[asys,,"prop"]
computes the property .

Details and OptionsDetails and Options

  • StateTransformationLinearize attempts to transform an affine system to a linear one so that linear control techniques can be used on the linearized dynamics.
  • Using a state transformation , the original affine system with dynamics and output gets transformed to an input-output, input-state, or state-output linear system.
  • The following forms of exact linearization lform can be used:
  • Automaticautomatically linearize
    "InputOutput",
    "InputState",
    "StateOutput",
  • The Automatic setting will attempt , , or .
  • StateTransformationLinearize returns a LinearizingTransformationData object that can be used to extract detailed properties for further analysis and design.
  • Properties related to the state transformation include:
  • "InverseStateTransformation"inverse state transformation
    "StateTransformation"state transformation
    "TransformedSystem"linearized or partially linearized transformed system tsys
    "Linearization"form of linearization
  • Properties related to controller and estimator design include:
  • {"OriginalSystemController",cs}controller for asys based on controller cs designed for tsys
    {"OriginalSystemEstimator",es}estimator for asys based on estimator es designed for tsys
    {"ClosedLoopSystem",cs}closed-loop system based on the linear controller cs

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Linearize an affine system using state transformation:

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The transformed system is completely linear:

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Compute feedback gains for the system, using the linearized system:

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The closed-loop system:

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The closed-loop system is stable:

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Introduced in 2014
(10.0)