李雅普诺夫方程的新解法  

A New Approach to the Solution of Lyapunov Equation

作　　者：塞拉斯 宋扬 孙华飞 MIRAU Silas;SONG Yang;SUN Hua-fei(School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China)

机构地区：[1]北京理工大学数学与统计学院,北京100081

出　　处：《北京理工大学学报》2020年第3期347-350,共4页Transactions of Beijing Institute of Technology

基　　金：北京市科委创新项目(Z161100005016043)。

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.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.

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 

分 类 号：O186[理学—数学]