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


  • The Kronecker decomposition is also known as the Weierstrass decomposition.
  • The result is a list , 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 is nilpotent:
  • continuous time
    discrete time
  • The output of the system in Kronecker form is:
  • continuous time
    discrete time
  • The matrices and are both taken to be in Jordan form.
  • StateSpaceTransform[ssm, {p, q}] has the form StateSpaceModel[{, , , , }], with and , where and are identity matrices with the dimensions of the slow and fast subsystems, and is a nilpotent matrix.
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