| Solutions to the generalized Sylvester matrix equations by a singular value decomposition |
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| 引用本文： | Bin ZHOU,Guangren DUAN. Solutions to the generalized Sylvester matrix equations by a singular value decomposition[J]. 控制理论与应用(英文版), 2007, 5(4): 397-403. DOI: 10.1007/s11768-006-6113-0 |
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| 作者姓名： | Bin ZHOU Guangren DUAN |
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| 作者单位： | Bin ZHOU（Center for Control Theory and Guidance Technology,Harbin Institute of Technology,Harbin Heilongjiang 150001,China） ;Guangren DUAN（Center for Control Theory and Guidance Technology,Harbin Institute of Technology,Harbin Heilongjiang 150001,China） ; |
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| 基金项目： | 国家优秀青年科学家基金，教育部长江学者和创新团队发展计划 |
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| 摘 要： | In this paper,solutions to the generalized Sylvester matrix equations AX-XF=BY and MXN-X=TY with A,M∈Rn×n,B,T∈Rn×n,F,N∈Rp×p and the matrices N,F being in companion form,are established by a singular value decomposition of a matrix with dimensions n×(n pr).The algorithm proposed in this paper for the euqation AX-XF=BY does not require the controllability of matrix pair(A,B)andthe restriction that A,F do not have common eigenvalues.Since singular value decomposition is adopted,the algorithm is numerically stable and may provide great convenience to the computation of the solution to these equations,and can perform important functions in many design problems in control systems theory.
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| 关 键 词： | 矩阵方程式 普遍性 西尔威斯特 计算机 |
| 收稿时间： | 2006-06-16 |
| 修稿时间： | 2006-11-22 |
Solutions to the generalized Sylvester matrix equations by a singular value decomposition |
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| Bin ZHOU,Guangren DUAN. Solutions to the generalized Sylvester matrix equations by a singular value decomposition[J]. Journal of Control Theory and Applications, 2007, 5(4): 397-403. DOI: 10.1007/s11768-006-6113-0 |
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| Authors: | Bin ZHOU Guangren DUAN |
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| Affiliation: | Center for Control Theory and Guidance Technology,Harbin Institute of Technology,Harbin Heilongjiang 150001,China |
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| Abstract: | |
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| Keywords: | Generalize Sylvester matrix equations General solutions Companion matrix Singular value decomposition |
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