| 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.[点击复制] |
| YU Hai-hua,DUAN Guang-ren.The analytical general solutions to the higher-order Sylvester matrices equation[J].Control Theory and Technology,2011,28(5):698~702.[点击复制] |
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| 高阶Sylvester矩阵方程的解析通解 |
| The analytical general solutions to the higher-order Sylvester matrices equation |
| 摘要点击 3544 全文点击 2040 投稿时间：2008-08-30 修订日期：2010-06-25 |
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| DOI编号 10.7641/j.issn.1000-8152.2011.5.CCTA081023 |
| 2011,28(5):698-702 |
| 中文关键词 矩阵方程 解析通解 特征值 若当标准型 |
| 英文关键词 matrix equation analytical general solution eigenvalue Jordan canonical form |
| 基金项目 国家杰出青年科学基金资助项目(69925308). |
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| 中文摘要 |
| 给出了矩阵方程A_{m1}V J^{m1} +...+A_1V J +A_0V = B_{m2}WJ^{m2} +...+B_1WJ +B_0W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解的有效性. |
| 英文摘要 |
| 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. |