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BUILT-IN MATHEMATICA SYMBOL
RiccatiSolve
RiccatiSolve[{a, b}, {q, r}]
gives the matrix 
that is the stabilizing solution of the continuous algebraic Riccati equation ![TemplateBox[{a}, ConjugateTranspose].x+x.a-x.b.TemplateBox[{r}, Inverse].TemplateBox[{b}, ConjugateTranspose].x+q=0](Files/RiccatiSolve.en/2.png "TemplateBox[{a}, ConjugateTranspose].x+x.a-x.b.TemplateBox[{r}, Inverse].TemplateBox[{b}, ConjugateTranspose].x+q=0"){kind=small}
.
RiccatiSolve[{a, b}, {q, r, p}]
solves the equation ![TemplateBox[{a}, ConjugateTranspose].x+x.a-(x.b+p).TemplateBox[{r}, Inverse].(TemplateBox[{b}, ConjugateTranspose].x+TemplateBox[{p}, ConjugateTranspose])+q=0](Files/RiccatiSolve.en/3.png "TemplateBox[{a}, ConjugateTranspose].x+x.a-(x.b+p).TemplateBox[{r}, Inverse].(TemplateBox[{b}, ConjugateTranspose].x+TemplateBox[{p}, ConjugateTranspose])+q=0"){kind=small}
.
Details and Options
- In
![TemplateBox[{a}, ConjugateTranspose].x+x.a-x.b.TemplateBox[{r}, Inverse].TemplateBox[{b}, ConjugateTranspose].x+q=0](Files/RiccatiSolve.en/4.png "TemplateBox[{a}, ConjugateTranspose].x+x.a-x.b.TemplateBox[{r}, Inverse].TemplateBox[{b}, ConjugateTranspose].x+q=0")
, 
denotes the conjugate transpose. - The equation
![TemplateBox[{a}, ConjugateTranspose].x+x.a-x.b.TemplateBox[{r}, Inverse].TemplateBox[{b}, ConjugateTranspose].x+q=0](Files/RiccatiSolve.en/6.png "TemplateBox[{a}, ConjugateTranspose].x+x.a-x.b.TemplateBox[{r}, Inverse].TemplateBox[{b}, ConjugateTranspose].x+q=0")
has a unique, symmetric, positive semidefinite solution 
if 
is stabilizable, 
is detectable, 
, and 
. Consequently, all eigenvalues of the matrix 
are negative and the solution is stabilizing. - The solution is positive definite when
is controllable and 
is observable. - The eigenvalues of the Hamiltonian matrix
![(a -b.TemplateBox[{r}, Inverse].b; -q -a)](Files/RiccatiSolve.en/15.png "(a -b.TemplateBox[{r}, Inverse].b; -q -a)")
must not contain any symbolic expressions. - RiccatiSolve supports a Method option. The following explicit settings can be specified:
-
"Eigensystem" use eigenvalue decomposition "Schur" use Schur decomposition - By default, eigenvalue decomposition is used to obtain the solution.
- The setting Method->"Schur" works only with approximate numerical matrices.
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