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[λ e - a]0 for some λ.


open allclose all

Basic Examples  (1)

The output controllability matrix of a state-space model:

Scope  (2)

The output controllability matrix of a continuous-time system:

A descriptor system:

Properties & Relations  (4)

A system is output controllable when the rank of the matrix equals 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 does not depend on the sampling period:

Introduced in 2010
Updated in 2012