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BUILT-IN MATHEMATICA SYMBOL
ControllabilityMatrix[ssm]
gives the controllability matrix of the state-space model ssm.
Details
- For a standard state-space model with state equations:
-
continuous-time system 
discrete-time system - The controllability matrix is computed as
, where 
is the dimension of 
. - For a descriptor state-space model with state equations:
-
continuous-time system 
discrete-time system - The slow and fast subsystems can be decoupled as described in KroneckerModelDecomposition:
-
slow subsystem 
fast subsystem - ControllabilityMatrix 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 controllability matrices only exist for descriptor systems in which Det[
e-a]≠0 for some .
New in 8 | Last modified in 9
