BUILT-IN MATHEMATICA SYMBOL

# KroneckerModelDecomposition

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

## DetailsDetails

• 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.

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Compute the Kronecker decomposition of a state-space model:

 Out[1]=