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OutputControllabilityMatrix

OutputControllabilityMatrix[ss]
gives the output controllability matrix of the StateSpaceModel object ss.
  • The state-space model ss can be given as StateSpaceModel, 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 computed as , where is the dimension of the square state matrix .
The output controllability matrix of a state-space model:
The output controllability matrix of a state-space model:
In[1]:=
Click for copyable input
Out[1]//MatrixForm=
The output controllability matrix of a continuous-time system:
A system is output controllable if and only if the rank of its output controllability matrix is equal to the number of outputs:
This system is not output-controllable but is state-controllable:
This system is output-controllable but not state-controllable:
The output controllability matrix of a discrete-time system does not depend on the sampling period:
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