## On the parametric solution to the second-order Sylvester matrix equation $$EVF^{2} - AVF - CV=BW$$.(English)Zbl 1160.15017

For a real diagonalizable matrix $$F$$, a controllable matrix triple $$(E,A,B)$$, and a given $$C$$, the authors describe a parametric solution $$V,W$$ for the second order Sylvester equation
$EVF^2 - AVF - CV = BW.$
If $$F$$ is not explicitly given, the solution is found by elementary transformations performed on respective matrix pencils and the solution depends on the eigenvalues of $$F$$, as well as on another set of parameters. If the eigenvalues of $$F$$ are prescribed, then the solution method involves the singular value decomposition.

### MSC:

 15A24 Matrix equations and identities 65F30 Other matrix algorithms (MSC2010) 93B40 Computational methods in systems theory (MSC2010) 93B05 Controllability
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### References:

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