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ObservableModelQ

ObservableModelQ[ss]
gives True if the StateSpaceModel object ss is observable, and False otherwise.
MORE INFORMATION
  • A state-space model is said to be observable if, for any initial time, the state vector can be determined from the outputs of the model, measured over a finite time.
  • accepts a Method option. The following settings can be specified:
"Matrix"tests if the observability matrix has full rank
"Gramian"tests if the observability Gramian is positive definite
"PBH"uses the Popov-Belevitch-Hautus rank test
  • With the default setting Method->Automatic, each method is evaluated in turn until the system is determined to be observable or all methods have been exhausted.
EXAMPLESCLOSE ALL
Basic Examples   (2)
An observable system:
An unobservable system:
An observable system:
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Click for copyable input
Out[1]=
 
An unobservable system:
In[1]:=
Click for copyable input
Out[1]=
Scope   (3)
Test if a continuous-time system is observable:
Test if a discrete-time system is observable:
An unobservable system:
Options   (3)
Verify observability using the observability matrix:
Use the observability Gramian:
Use the PBH rank test:
Possible Issues   (1)
The Gramian method is not reliable for systems that are not asymptotically stable:
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