A class of fixed point iteration for the coupled algebraic Riccati equation

被引：3
|
作者：
Zhang, Juan [1 ]
Liu, Jianzhou [1 ]
Luo, Fangfang [1 ]
机构：
[1] Xiangtan Univ, Dept Math & Computat Sci, Key Lab Intelligent Computine & Informat Proc, Minist Educ,Hunan Key Lab Computat & Simulat Sci, Xiangtan 411105, Hunan, Peoples R China
来源：
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING | 2022年 / 68卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Fixed point iterative method; Positive solution; Coupled Riccati equation; ALGORITHM; INVARIANT; BOUNDS;
D O I：
10.1007/s12190-021-01697-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the positive solution of the coupled algebraic Riccati equation. If this equation has a positive solution, the existence and convergence rate for the solution is discussed. Additionally, we show special properties for the positive solution of this equation. Further, a fixed point iteration method for the minimal positive solution of the coupled algebraic Riccati equation is proposed. Finally, we offer corresponding numerical examples to show the effectiveness of the derived results.
引用
收藏
页码：4119 / 4133
页数：15
相关论文
共 50 条
  • [1] A class of fixed point iteration for the coupled algebraic Riccati equation
    Juan Zhang
    Jianzhou Liu
    Fangfang Luo
    [J]. Journal of Applied Mathematics and Computing, 2022, 68 : 4119 - 4133
  • [2] The matrix bounds and fixed-point iteration for the solution of the discrete algebraic Riccati equation
    Zhang, Juan
    Liu, Jianzhou
    [J]. IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 2019, 36 (02) : 681 - 699
  • [3] ANALYSIS OF AN ITERATION METHOD FOR THE ALGEBRAIC RICCATI EQUATION
    Massoudi, Arash
    Opmeer, Mark R.
    Reis, Timo
    [J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2016, 37 (02) : 624 - 648
  • [4] Fixed-Point Iteration Schemes to Solve Symmetric Algebraic Riccati Equation XBX - XA - ATX - C=0
    Erfanifar, Raziyeh
    Hajarian, Masoud
    [J]. CIRCUITS SYSTEMS AND SIGNAL PROCESSING, 2024, 43 (06) : 3516 - 3532
  • [5] Modified Alternately Linearized Implicit Iteration Methods for Nonsymmetric Coupled Algebraic Riccati Equation
    Wang, Li
    Xiao, Yi
    Zhu, Yu-Li
    Wang, Yi-Bo
    [J]. COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, 2024,
  • [6] The solution bounds and fixed point iterative algorithm for the discrete coupled algebraic Riccati equation applied to automatic control
    Liu, Jianzhou
    Wang, Li
    Zhang, Juan
    [J]. IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION, 2017, 34 (04) : 1135 - 1156
  • [7] A new subspace iteration method for the algebraic Riccati equation
    Lin, Yiding
    Simoncini, Valeria
    [J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2015, 22 (01) : 26 - 47
  • [8] Matrix bounds for the coupled algebraic Riccati equation
    Gao, LX
    Xue, A
    Sun, YX
    [J]. PROCEEDINGS OF THE 4TH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION, VOLS 1-4, 2002, : 180 - 183
  • [9] The existence uniqueness and the fixed iterative algorithm of the solution for the discrete coupled algebraic Riccati equation
    Liu, Jianzhou
    Zhang, Juan
    [J]. INTERNATIONAL JOURNAL OF CONTROL, 2011, 84 (08) : 1430 - 1441
  • [10] ON THE SOLUTION OF A CLASS OF ALGEBRAIC MATRIX RICCATI EQUATION
    PEARCE, CEM
    [J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1986, 31 (03) : 252 - 255
12345