ON SOLVING THE LYAPUNOV AND STEIN EQUATIONS FOR A COMPANION MATRIX

被引：28

作者：

BETSER, A ^{[1
]}

COHEN, N ^{[1
]}

ZEHEB, E ^{[1
]}

机构：

[1] TECHNION ISRAEL INST TECHNOL,DEPT ELECT ENGN,IL-32000 HAIFA,ISRAEL

来源：

SYSTEMS & CONTROL LETTERS | 1995年 / 25卷 / 03期

关键词：

LYAPUNOV EQUATION; STEIN EQUATION; COMPUTATIONAL ASPECTS; HURWITZ MATRIX; KRONECKER PRODUCTS;

D O I：

10.1016/0167-6911(94)00072-4

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

When the matrix A is in companion form, the essential step in solving the Lyapunov equation PA + A(T)P = -Q involves a linear n x n system for the first column of the solution matrix P. The complex dependence on the data matrices A and Q renders this system unsuitable for actual computation. In this paper we derive an equivalent system which exhibits simpler dependence on A and Q as well as improved complexity and robustness characteristics. A similar result is obtained also for the Stein equation P - A(T)PA = Q.

引用

页码：211 / 218

页数：8