ObservableModelQ

ObservableModelQ[sys]

gives True if the system sys is observable, and False otherwise.

ObservableModelQ[{sys,sub}]

gives True if the subsystem sub is observable.

Details and Options

  • A state-space model is said to be observable at if the trajectory of the model from is distinguishable from that of another state in its neighborhood in finite time.
  • The system sys can be a standard or descriptor StateSpaceModel or AffineStateSpaceModel.
  • The following subsystems sub can be specified:
  • Allwhole system
    "Fast"fast subsystem
    "Slow"slow subsystem
    "Unstable"unstable subsystem
    {λ1,}subsystem with eigenmodes lambda_(i)
  • The "Fast" and "Slow" subsystems primarily apply to descriptor state-space models as described in KroneckerModelDecomposition.
  • The eigenmodes λi are described in JordanModelDecomposition.
  • ObservableModelQ accepts a Method option with the following settings:
  • Automaticautomatically choose the appropriate test
    "Distribution"use observability distribution's rank
    "Gramian"use observability Gramian's rank or positive definiteness
    "Matrix"use observability matrix's rank
    "PBH"use PopovBelevitchHautus rank test

Examples

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Basic Examples  (2)

An observable system:

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An unobservable system, since the second state is not observable:

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Scope  (6)

Options  (6)

Applications  (2)

Properties & Relations  (6)

Possible Issues  (1)

Introduced in 2010
(8.0)
|
Updated in 2014
(10.0)