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		Aiguo WU,Guangren DUAN,Bin ZHOU.[en_title][J].Control Theory and Technology,2007,5(1):47~52.[Copy]

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AiguoWU,GuangrenDUAN,BinZHOU
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Received:June 06, 2005Revised:April 12, 2006

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An explicit solution to the matrix equation AV+BW=EVJ

Aiguo WU, Guangren DUAN, Bin ZHOU

(Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin Heilongjiang 150001, China)

Abstract:

In this note, the matrix equation AV+BW=EVJ is considered, where E,Aand B are given matrices of appropriate dimensions, J is an arbitrarily given Jordan matrix, V and W are the matrices to be determined. Firstly, a right factorization of (sE-A)^{-1^B} is given based on the Leverriver algorithm for descriptor systems. Then based on this factorization and a proposed parametric solution, an alternative parametric solution to this matrix equation is established in terms of the R-controllability matrix of (E,A,B), the generalized symmetric operator and the observability matrix associated with the Jordan matrix J and a free parameter matrix. The proposed results provide great convenience for many analysis and design problems. Moreover, some equivalent forms are proposed. A numerical example is employed to illustrate the effect of the proposed approach.

Key words: Generalized Sylvester matrix equations Parametric solution R-controllability Leverriver algorithm