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Solving the generalized Sylvester matrix equation \(AV+BW=EVF\) via a Kronecker map. (English) Zbl 1221.65109

The authors present a closed-form solution to the generalized Sylvester matrix equation \(AV+BW=EVF\), with a help of the Kronecker map. The solution is explicitly expressed with the matrix \(F\) and a parameter matrix and hence presents some convenience and advantages for practical applications such as the eigenstructure assignment for linear systems and the design of observer for descriptor systems.

MSC:

65F30 Other matrix algorithms (MSC2010)
15A24 Matrix equations and identities
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