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Kronecker Maps and Sylvester-Polynomial Matrix Equations

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3 Author(s)
Ai-Guo Wu ; Center for Control Theor. & Guidance Tech, Harbin Inst. of Technol. ; Guang-Ren Duan ; Yu Xue

The concepts of Kronecker maps and Sylvester-polynomial matrix equations are proposed. Some properties of the Kronecker maps are deduced. It is shown that many kinds of matrix equations can be formulated into the so-called Sylvester-polynomial matrix equations. With the help of the Kronecker maps, general explicit solutions of the Sylvester-polynomial matrix equations are established when the polynomial matrices possess F-primeness. For the nonsquare case, the proposed solutions can offer all the degrees of freedom represented by a free parameter matrix

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Automatic Control, IEEE Transactions on  (Volume:52 ,  Issue: 5 )