yields True if the state-space model sys is controllable, and False otherwise.


yields True if the subsystem sub is controllable.

Details and Options

  • ControllableModelQ is also known as a reachable model.
  • A state-space model is said to be controllable if for any initial state and any final state there exists some control input that drives the state from to in finite time.
  • The system sys can be a standard or descriptor StateSpaceModel or AffineStateSpaceModel.
  • The following subsystems sub can be specified: »
  • Allwhole system
    "Fast"fast subsystem
    "Slow"slow subsystem
    {λ1,}subsystem with eigenmodes
  • The "Fast" and "Slow" subsystems primarily apply to descriptor state-space models as described in KroneckerModelDecomposition.
  • The eigenmodes λi are described in JordanModelDecomposition.
  • ControllableModelQ accepts a Method option with the following settings:
  • Automaticautomatically choose the appropriate test
    "Distribution"use controllability distribution's rank
    "Gramian"use controllability Gramian's rank or positive definiteness
    "Matrix"use controllability matrix's rank
    "PBH"use PopovBelevitchHautus rank test


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Basic Examples  (2)

A controllable system:

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An uncontrollable system, since there is no way to affect the second state:

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Scope  (6)

Options  (7)

Applications  (5)

Properties & Relations  (7)

Possible Issues  (2)

Introduced in 2010
Updated in 2014