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"test if the observability codistribution has full rank
    "Gramian"test if the observability Gramian is positive definite
    "Matrix"test if the observability matrix has full rank
    "PBH"use the PopovBelevitchHautus rank test

Examples

open allclose all

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)

See Also

ObservabilityMatrix  ObservabilityGramian  JordanModelDecomposition  KroneckerModelDecomposition

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