gives the output controllability matrix of the state-space model ssm.


  • 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 .
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