| 李雅普诺夫方程的新解法 |
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| 引用本文： | 塞拉斯,宋扬,孙华飞. 李雅普诺夫方程的新解法[J]. 北京理工大学学报, 2020, 40(3): 347-350. DOI: 10.15918/j.tbit1001-0645.2018.356 |
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| 作者姓名： | 塞拉斯 宋扬 孙华飞 |
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| 作者单位： | 北京理工大学 数学与统计学院, 北京 100081 |
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| 基金项目： | 北京市科委创新项目（Z161100005016043） |
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| 摘 要： | 利用对数欧氏度量的方法给出李雅普诺夫方程的新解法.介绍了李雅普诺夫方程的由来,介绍对称正定矩阵流形的黎曼度量以及对数欧氏度量下的距离函数,给出求解李雅普诺夫方程的迭代公式,并给出模拟仿真的结果.
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| 关 键 词： | 李雅普诺夫方程 对数欧氏度量 对称正定矩阵流形 黎曼度量 |
| 收稿时间： | 2018-06-27 |
A New Approach to the Solution of Lyapunov Equation |
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| MIRAU Silas,SONG Yang and SUN Hua-fei. A New Approach to the Solution of Lyapunov Equation[J]. Journal of Beijing Institute of Technology(Natural Science Edition), 2020, 40(3): 347-350. DOI: 10.15918/j.tbit1001-0645.2018.356 |
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| Authors: | MIRAU Silas SONG Yang SUN Hua-fei |
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| Affiliation: | School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, China |
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| Abstract: | A new approach was proposed based on the Log-Euclidean metric to solve the Lyapunov equation. First, the origin of Lyapunov equation was introduced. Then the Riemannian metrics on a manifold of symmetric positive definite matrices and the geodesic distance function under Log-Euclidean metric were presented. Last, the iterative formula for the solution to Lyapunov equation was obtained, and some simulation results were shown. |
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| Keywords: | Lyapunov equation Log-Euclidean metric symmetric positive definite manifold Riemannian metric |
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