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Legacy Documentation

Mathematica 8 (2010)

This is documentation for Mathematica 8, which was
based on an earlier version of Wolfram Language.
View current documentation (Version 14.3)

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.
(1)
The controllability matrix of a state-space model:
The controllability matrix of a state-space model:
Out[1]//MatrixForm=
(2)
The controllability matrix of a continuous-time system:
The computation depends only on the state and input matrix:
(4)
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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