Projected generalized discrete-time periodic Lyapunov equations and balanced realization of periodic descriptor systems

被引：38
作者：
Chu, Eric King-Wah
Fan, Hung-Yuan
Lin, Wen-Wei
机构：
[1] Monash Univ, Sch Math Sci, Clayton, Vic 3168, Australia
[2] Hsuan Chuang Univ, Dept Math Appl, Hsinchu 300, Taiwan
[3] Natl Tsing Hua Univ, Dept Math, Hsinchu 300, Taiwan
来源：
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2007年 / 29卷 / 03期
关键词：
periodic systems; descriptor systems; reachability and observability Gramians; Hankel singular values; balanced realization;
D O I：
10.1137/040606715
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
From the necessary and sufficient conditions for complete reachability and observability of periodic descriptor systems with time-varying dimensions, the symmetric positive semidefinite reachability/observability Gramians are defined. These Gramians can be shown to satisfy some projected generalized discrete-time periodic Lyapunov equations. We propose a numerical method for solving these projected Lyapunov equations, and give an illustrative numerical example. As an application of our results, the balanced realization of periodic descriptor systems is discussed.
引用
收藏
页码：982 / 1006
页数：25
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