The solution bounds and fixed point iterative algorithm for the discrete coupled algebraic Riccati equation applied to automatic control

被引：6

作者：

Liu, Jianzhou ^{[1
]}

Wang, Li ^{[1
]}

Zhang, Juan ^{[1
,2
]}

机构：

[1] Xiangtan Univ, Dept Math & Computat Sci, Xiangtan 411105, Hunan, Peoples R China

[2] Natl Univ Def Technol, Coll Sci, Changsha 410073, Hunan, Peoples R China

来源：

IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION | 2017年 / 34卷 / 04期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

matrix bound; discrete coupled algebraic Riccati equation; eigenvalue; MATRIX EQUATION;

D O I：

10.1093/imamci/dnw012

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this article, applying the special properties of nonnegative matrices and symmetric matrices, we consider the coupled term as a whole and derive the solution bounds of the discrete coupled algebraic Riccati equation. This reduces the error of taking apart the coupled term separately when applying inequality techniques to get the bounds in general. Then, using Cauchy-Schwarz inequality, matrix norm inequalities and a fixed point theorem, we discuss the existence uniqueness condition and fixed point iteration for the solution of this equation. Finally, we offer corresponding numerical examples to illustrate the effectiveness of our results.

引用

页码：1135 / 1156

页数：22

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