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BUILT-IN MATHEMATICA SYMBOL
JordanModelDecomposition
JordanModelDecomposition[ssm]
yields the Jordan decomposition of the state-space model ssm.
Details
- The result is a list
, where p is a similarity matrix, and jc is the Jordan canonical form of ssm. - The state-space model ssm can be given as StateSpaceModel[{a, b, c, d}], where a, b, c, and d represent the state, input, output, and transmission matrices in either a continuous-time or a discrete-time system:
-
continuous-time system 
discrete-time system - The transformation
, where 
is the new state vector, and 
is a similarity matrix that spans the linearly independent eigenvectors of 
, transforms the system into the Jordan canonical form: -
![w'(t)=TemplateBox[{p}, Inverse].a.s.w(t)+TemplateBox[{p}, Inverse].b.u(t)](Files/JordanModelDecomposition.en/8.png "w'(t)=TemplateBox[{p}, Inverse].a.s.w(t)+TemplateBox[{p}, Inverse].b.u(t)")
, 
continuous-time system ![w(k+1)=TemplateBox[{p}, Inverse].a.p.w(k)+TemplateBox[{p}, Inverse].b.u(k)](Files/JordanModelDecomposition.en/10.png "w(k+1)=TemplateBox[{p}, Inverse].a.p.w(k)+TemplateBox[{p}, Inverse].b.u(k)")
,
.discrete-time system - The new state matrix
![TemplateBox[{p}, Inverse].a.p](Files/JordanModelDecomposition.en/12.png "TemplateBox[{p}, Inverse].a.p")
is the Jordan canonical form of the old state matrix 
.
Examplesopen all
Basic Examples (1)
Compute the Jordan decomposition of a state-space model:
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