数学
李雅普诺夫方程
李雅普诺夫函数
基质(化学分析)
数学分析
应用数学
纤维束
捆绑
计算机科学
量子力学
物理
非线性系统
复合材料
材料科学
作者
Aung Naing Win,Mingming Li
标识
DOI:10.1016/j.matcom.2021.10.031
摘要
In this paper, we firstly introduce the origin of Lyapunov matrix equation, and then the geometric methods for solving Lyapunov equation are given by using the Log-Euclidean metric and the fiber bundle-based Riemannian metric based on the manifold of positive definite Hermitian matrices. Then, the solution of Lyapunov matrix equation is presented by providing a natural gradient descent algorithm (NGDA), a Log-Euclidean descent algorithm (LGDA) and a Riemannian gradient algorithm based on fiber bundle (RGA). At last, the convergence speeds of the RGA, the NGDA and the LGDA are compared via two simulation examples. Simulation results show that the convergence speed of the RGA is faster than both of the LGDA and the NGDA.
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