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		Aiguo WU,Siming ZHAO,Guangren DUAN.[en_title][J].Control Theory and Technology,2008,6(3):330~332.[Copy]

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AiguoWU,SimingZHAO,GuangrenDUAN
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Received:April 18, 2006Revised:September 26, 2007

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Solving the generalized Sylvester matrix equation AV +BW = VF via Kronecker map

Aiguo WU, Siming ZHAO, Guangren DUAN

(Institute for Information and Control, Harbin Institute of Technology Shenzhen Graduate School, Shenzhen Guangdong 518055, China; Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin Heilongjiang 150001, China)

Abstract:

This note considers the solution to the generalized Sylvester matrix equation AV + BW = V F with F being an arbitrary matrix, where V and W are the matrices to be determined. With the help of the Kronecker map, an explicit parametric solution to this matrix equation is established. The proposed solution possesses a very simple and neat form, and allows the matrix F to be undetermined.

Key words: Kronecker map Sylvester matrix equation Parametric solution