gives a linearized state space to the model model at an equilibrium.


linearizes at state values {x10,} and input values {u10,}.

Details and Options

  • SystemModelLinearize gives a linear system, typically used for control design.
  • The model can be a SystemModel object, a full model name string or a shortened model name accepted by SystemModel.
  • SystemModelLinearize linearizes a continuous-time system from model.
  • SystemModelLinearize returns a StateSpaceModel object.
  • SystemModelLinearize[model,spec] allows the following symbolic values for spec:
  • "EquilibriumValues"uses FindSystemModelEquilibrium[model]
    "InitialValues"uses SystemModel[model]["GroupedInitialValues"]
  • SystemModelLinearize[model,vals,spec] uses spec to add missing values in vals.
  • The default spec is taken to be "EquilibriumValues".
  • The resulting StateSpaceModel has states xi, inputs uj and outputs yk as defined in model.
  • The list of states, inputs and outputs can be found from SystemModel[model,spec]:
  • "StateVariables"state variables xi
    "InputVariables"input variables uj
    "OutputVariables"output variables yk
  • SystemModelLinearize reduces a system of DAEs to a system of ODEs and linearizes the resulting ODEs.
  • A system of ODEs with state equations and output equations is linearized at a point and .
  • The linearized system has state , input and output , with state equations and output equation . The matrices are given by , , and , all evaluated at and .
  • The returned StateSpaceModel corresponds to the system , .
  • The following options can be given:
  • Method"NumericDerivative"methods for linearization algorithm
    SystemModelProgressReportingAutomaticcontrol display of progress
  • The option Method has the following possible settings:
  • "NumericDerivative"uses SystemModeler linearization
    "SymbolicDerivative"uses StateSpaceModel linearization


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Basic Examples  (3)

Linearize a DC-motor model around an equilibrium:

Click for copyable input

Linearize a mixing tank model around equilibrium with given state and input constraints:

Click for copyable input

Linearize one of the included introductory hierarchical examples:

Click for copyable input
Click for copyable input

Scope  (13)

Generalizations & Extensions  (1)

Options  (4)

Applications  (10)

Properties & Relations  (8)

Possible Issues  (1)

See Also

StateSpaceModel  SystemModel  FindSystemModelEquilibrium  SystemModelSimulate  SystemModelExamples

Introduced in 2018