yields the Kronecker decomposition of a descriptor state-space model ssm.

Details and Options

  • The Kronecker decomposition is also known as the Weierstrass decomposition.
  • The result is a list {{p,q},kssm}, where p and q are transformation matrices, and kssm is the Kronecker form of ssm.
  • The decomposition decouples a descriptor state-space model into slow and fast subsystems.
  • The slow subsystem has the same form as a standard state-space model with state equation:
  • continuous time
    discrete time
  • The fast subsystem is governed by the following state equations where e2 is nilpotent:
  • continuous time
    discrete time
  • The output of the system in Kronecker form is:
  • continuous time
    discrete time
  • The matrices a1 and e2 are both taken to be in Jordan form.
  • StateSpaceTransform[ssm,{p,q}] has the form StateSpaceModel[{,,,,}], with and , where and a2 are identity matrices with the dimensions of the slow and fast subsystems, and is a nilpotent matrix.


open allclose all

Basic Examples  (1)

Compute the Kronecker decomposition of a state-space model:

Click for copyable input

Scope  (4)

Applications  (2)

Properties & Relations  (6)

See Also

StateSpaceTransform  JordanDecomposition  ControllableDecomposition  ObservableDecomposition  StateSpaceModel

Introduced in 2012