求解规范型Lyapunov矩阵方程的新方法

A NEW METHOD FOR SOLVING LYAPUNOV MATRIX EQUATIONS IN CANONICAL FORMS

本文揭示了规范型Lyapunov矩阵方程及其对偶方程的一些特殊性质,充分压缩解矩阵的未知元素,并利用对偶解矩阵与解矩阵的合同关系,提出了一种高精度、高效率求解规范型Lyapunov方程的新算法,文中举例验证了新算法的正确性。 Lyapunov矩阵方程 能控制和能观测规范型

In this paper, some special properties of Lyapunov matrix equation and its dual equation in canonical forms are discussed. By sufficiently reducing unknown elements of solution matrix, and using the relationship that dual solution matrix is congruent with solution matrix, an efficient and accurate new method for solving Lyapunov matrix equation in canonieal forms is presented. The method is verified bv examples.