 |
BUILT-IN MATHEMATICA SYMBOL
ObservabilityMatrix[ssm]
gives the observability matrix of the state-space model ssm.
Details
- For a standard state-space model:
-
continuous-time system 
discrete-time system - The observability matrix is given by
, where 
is the dimension of 
. - For a descriptor state-space model:
-
continuous-time system 
discrete-time system - The slow and fast subsystems can be decoupled as described in KroneckerModelDecomposition:
-
slow subsystem 
fast subsystem 
output equation - ObservabilityMatrix returns a pair of matrices
, based on the decoupled slow and fast subsystems. The matrices 
and 
are defined as follows, where 
is the dimension of 
, and 
is the nilpotency index of 
. -
slow subsystem 
fast subsystem - The observability matrices only exist for descriptor systems in which Det[
e-a]≠0 for some .
Examplesopen all
Basic Examples (1)
The observability matrix of a state-space model:
| In[1]:= |
Out[1]//MatrixForm= | |
 | |
New in 8 | Last modified in 9
