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"test if the controllability distribution has full rank
    "Gramian"test if the controllability Gramian is positive definite
    "Matrix"test if the controllability matrix has full rank
    "PBH"use the PopovBelevitchHautus rank test


open allclose all

Basic Examples  (2)

A controllable system:

Click for copyable input

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

Click for copyable input

Scope  (6)

Options  (7)

Applications  (5)

Properties & Relations  (7)

Possible Issues  (2)

See Also

OutputControllableModelQ  ControllabilityMatrix  ControllabilityGramian  JordanModelDecomposition  KroneckerModelDecomposition

Introduced in 2010
| Updated in 2014