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BUILT-IN MATHEMATICA SYMBOL
KroneckerModelDecomposition
KroneckerModelDecomposition[ssm]
yields the Kronecker decomposition of a descriptor state-space model ssm.
Details
- 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.
Examplesopen all
Basic Examples (1)
Compute the Kronecker decomposition of a state-space model:
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