ControllabilityMatrix

ControllabilityMatrix[ssm]
gives the controllability matrix of the state-space model ssm.

DetailsDetails

  • 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[λ e-a]0 for some λ.

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

The controllability matrix of a state-space model:

In[1]:=
Click for copyable input
Out[1]//MatrixForm=

The controllability multi-input state-space model:

In[1]:=
Click for copyable input
Out[1]//MatrixForm=
Introduced in 2010
(8.0)
| Updated in 2012
(9.0)