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BUILT-IN MATHEMATICA SYMBOL
ObservabilityGramian[ssm]
gives the observability Gramian of the state-space model ssm.
Details and Options
- The state-space model ssm can be given as StateSpaceModel[{a, b, c, d}], where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:
-
continuous-time system 
discrete-time system - The observability Gramian:
-
continuous-time system 
discrete-time system - For asymptotically stable systems, the Gramian
can be computed as the solution of a Lyapunov equation: -
continuous-time system 
discrete-time system - For a StateSpaceModel with a descriptor matrix, ObservabilityGramian returns a pair of matrices
, where 
is associated with the slow subsystem, and 
is associated with the fast subsystem. - The controllability Gramians only exist for descriptor systems in which Det[
e-a]≠0 for some .
Examplesopen all
Basic Examples (1)
The observability Gramian of a system:
| In[1]:= |
| Out[1]= |  |
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