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ControllabilityMatrix

ControllabilityMatrix[ss]
gives the controllability matrix of the StateSpaceModel object ss.
  • The state-space model ss can be given as StateSpaceModel, where a and b represent the state and input matrices in either the continuous-time system or the discrete-time system:
continuous-time system
discrete-time system
  • The controllability matrix is computed as , where n is the dimension of the square state matrix a.
The controllability matrix of a state-space model:
The controllability matrix of a state-space model:
In[1]:=
Click for copyable input
Out[1]//MatrixForm=
The controllability matrix of a continuous-time system:
The computation depends only on the state and input matrix:
A system is controllable if and only if its controllability matrix has full rank:
This system is not controllable but is output-controllable:
This system is controllable but is not output-controllable:
The controllability matrix of a discrete-time system does not depend on the sampling period:
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