| 高阶Sylvester矩阵方程的解析通解 |
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| 引用本文： | 于海华,段广仁.高阶Sylvester矩阵方程的解析通解[J].控制理论与应用,2011,28(5):698-702. |
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| 作者姓名： | 于海华 段广仁 |
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| 作者单位： | 1. 黑龙江大学自动化系,黑龙江哈尔滨150080;哈尔滨工业大学控制理论与制导技术研究中心,黑龙江哈尔滨150001
2. 哈尔滨工业大学控制理论与制导技术研究中心,黑龙江哈尔滨,150001 |
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| 基金项目： | 国家杰出青年科学基金资助项目(69925308). |
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| 摘 要： | 给出了矩阵方程Am1 VJm1+…+A1VJ+A0V=Bm2 WJm2+…+B1WJ+BoW的3种完全解析参数通解.这些解由一组参数向量给出,这些参数向量提供了问题的全部自由度.求解算法不要求矩阵J具有不同的特征值,或者和A(s)的特征值不同.这些通解仅包含数值矩阵计算,为工程应用计算提供了方便.算例说明本文所给方程通...
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| 关 键 词： | 矩阵方程 解析通解 特征值 若当标准型 |
| 收稿时间： | 2008/8/30 0:00:00 |
| 修稿时间： | 2010/6/25 0:00:00 |
The analytical general solutions to the higher-order Sylvester matrices equation |
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| YU Hai-hua and DUAN Guang-ren.The analytical general solutions to the higher-order Sylvester matrices equation[J].Control Theory & Applications,2011,28(5):698-702. |
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| Authors: | YU Hai-hua and DUAN Guang-ren |
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| Affiliation: | Department of Automation, Heilongjiang University; Center for Control Theory and Guidance Technology, Harbin Institute of Technology,Center for Control Theory and Guidance Technology, Harbin Institute of Technology |
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| Abstract: | Three completely analytical parametric solutions to the matrices equation A_{m1}V J^{m1} +...+A_1V J +A_0V = B_{m2}WJ^{m2} +...+B_1WJ +B_0W are presented. These solutions are expressed in terms of parameter vectors, which provide the design degrees of freedom. These approaches do not require the eigenvalues of J to be distinct or to be different from the roots of A(s). Moreover, the obtained solutions contain only numerical matrix calculations, which provide convenience for the computation of these solutions in applications. A numerical example validates the proposed approaches. |
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| Keywords: | matrix equation analytical general solution eigenvalue Jordan canonical form |
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