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ControllableDecomposition

ControllableDecomposition[ss]
yields the controllable decomposition of the StateSpaceModel object ss. The result is a list where is the transformation matrix and is the controllable subspace of 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
  • For continuous-time systems, the transformation , where is the subspace spanned by the controllability matrix, yields the controllable subspace of the system as , .
  • The similarity transformation , where is the uncontrollable subspace, gives the Kalman controllable form , of the system.
Compute the controllable subsystem of a third-order system:
The transformation matrix selects the controllable subsystem:
Compute the controllable subsystem of a third-order system:
In[1]:=
Click for copyable input
Out[1]=
The transformation matrix selects the controllable subsystem:
In[2]:=
Click for copyable input
Out[2]=
The controllable subspace of a controllable system is the complete system:
The controllable subspace of partially controllable systems:
A function that constructs the Kalman controllable form of a state-space model:
A function that gives the dimension of the controllable subspace:
A function that returns sublists of controllable and uncontrollable modes:
The transformation matrix selects the controllable subsystem:
The transform using the transposed matrix returns the original system:
ControllableDecomposition returns unevaluated for a system with no controllable modes:
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