 |
BUILT-IN MATHEMATICA SYMBOL
OutputControllabilityMatrix
OutputControllabilityMatrix[ssm]
gives the output controllability matrix of the state-space model ssm.
Details
- 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 output controllability matrix is given by
, where 
is the dimension of the square state matrix 
. - For a descriptor state-space model, OutputControllabilityMatrix returns a matrix
where 
is associated with the slow subsystem and 
is associated with the fast subsystem. - For StateSpaceModel[{a, b, c, d, e}] with singular descriptor matrix e, the output controllability matrix is computed by decoupling the slow and fast subsystems:
-
slow subsystem 
fast subsystem 
output equation - The output controllability matrix where
has nilpotency index 
is given by 
. - OutputControllabilityMatrix only takes descriptor systems in which Det[
e - a]≠0 for some .
Examplesopen all
Basic Examples (1)
The output controllability matrix of a state-space model:
| In[1]:= |
Out[1]//MatrixForm= | |
 | |
New in 8 | Last modified in 9
