Inverse and Direct Solutions of the Discrete Time Lyapunov Equation With System Matrix in Companion Form

被引：0

作者：

Kanellakis, Apostolos ^{[1
]}

Tawfik, Ayman ^{[2
]}

Agathoklis, Panajotis ^{[3
]}

机构：

[1] Natl Tech Univ Athens, Sch Elect & Comp Engn, Athens 15780, Greece

[2] Ajman Univ, Coll Engn & Informat Technol, Dept Elect & Comp Engn, Ajman, U Arab Emirates

[3] Univ Victoria, Dept Elect & Comp Engn, Victoria, BC V8W 5C2, Canada

来源：

IEEE ACCESS | 2021年 / 9卷

关键词：

Discrete systems; Lyapunon matrix equation; stability table; companion matrix form; Mansour matrix form; FISHERS INFORMATION MATRIX; STEIN EQUATIONS; GENERALIZED SYLVESTER; ALGORITHMS;

D O I：

10.1109/ACCESS.2021.3136909

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The discrete time Lyapunov equation is used in many applications and there is interest in its inverse and direct solutions. New methods are proposed to obtain solutions for cases where the system matrix is in controllable canonical form. The approach is based on the relationship between the discrete Lyapunov equation and the entries of one of the stability tables presented by Jury. It is shown that the inverse solution, which is based on this stability table, can be obtained using LDLt decomposition. Also the direct solution of the discrete Lyapunov equation can be obtained directly from the entries of this stability table. The proposed algorithms are illustrated by numerical examples.

引用

页码：168397 / 168403

页数：7

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