CarlemanLinearize

CarlemanLinearize[sys,spec]
Carleman linearizes the nonlinear state-space model sys according to spec.

DetailsDetails

  • CarlemanLinearize gives an approximation of the infinite order system in which sys is embedded.
  • For input-linear systems, the result is bilinear, that is, linear in both the states and inputs. In general, it is linear only in the states.
  • Possible values for spec:
  • kapproximation order
    {{e1,,en}}monomials of the embedding transformation
    {,{z1,,zn}}new state variables
    {,z,order}monomial ordering
  • Possible settings for order are the same as in MonomialList.
  • CarlemanLinearize returns a LinearizingTransformationData object that can be used to extract various properties.
  • The following properties can be given:
  • "EmbeddingTransformation"
    "TransformedSystem"approximate transformed system
    {"OriginalSystemController",κ}controller for the original system sys
    {"OriginalSystemEstimator",}estimator for the original system sys
    {"ClosedLoopSystem",κ}closed-loop system of sys with the controller

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Carleman linearize a nonlinear system:

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Design a controller based on the linearized model:

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The closed-loop system:

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Simulate the closed-loop system:

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Introduced in 2014
(10.0)