A relation between the weighted logarithmic norm of a matrix and the Lyapunov equation

被引：25

作者：

Hu, GD

机构：

[1] Mem Univ Newfoundland, Dept Comp Sci, St Johns, NF A1B 3X5, Canada

[2] Univ Toronto, Dept Elect & Comp Engn, Syst Control Grp, Toronto, ON M5G 3G4, Canada

来源：

BIT NUMERICAL MATHEMATICS | 2000年 / 40卷 / 03期

关键词：

weighted logarithmic norm; Lyapunov equation; stable matrix;

D O I：

10.1023/A:1022380116022

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this note, we define a weighted logarithmic norm for any matrix. In the case when a stable matrix A is considered, we obtain the relationship between the maximal eigenvalue of a symmetric positive definite matrix H which is a solution of the Lyapunov equation and the weight H logarithmic norm of A. It can be seen that the weighted logarithmic norm of A is always a negative value in this case. Several examples illustrate the relationship.

引用

页码：606 / 610

页数：5

共 7 条

[1] Methods for linear systems of circuit delay differential equations of neutral type [J].