Closed-form solution of non-symmetric algebraic Riccati matrix equation

被引：11

作者：

Shirilord, Akbar ^{[1
]}

Dehghan, Mehdi ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran Polytech, 424 Hafez Ave, Tehran 15914, Iran

来源：

APPLIED MATHEMATICS LETTERS | 2022年 / 131卷

关键词：

Non-symmetric algebraic Riccati equation; Root of a matrix; Closed-form expression; ITERATIVE ALGORITHM; SHIFT PARAMETERS; IDENTIFICATION; LYAPUNOV; STATE;

D O I：

10.1016/j.aml.2022.108040

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we obtain closed-form expression for the solution of non-symmetric algebraic Riccati equation (NARE), AX + XB + XCX = D, A, B, C, D is an element of C-n Chi n, under some conditions on the matrices A, B, C and D. We show that the solution (real and complex) of this NARE is X = (root A(2) + DC - A)C-1, where root M is square root of matrix M. Finally this formula applied on some NAREs. (c) 2022 Elsevier Ltd. All rights reserved.

引用

页数：10

共 50 条

[21] ON THE SOLUTION OF A CLASS OF ALGEBRAIC MATRIX RICCATI EQUATION
PEARCE, CEM
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1986, 31 (03) : 252 - 255
[22] Development of a Closed-Form Solution for Instantaneous Threshold Optimization Using Modified Riccati Equation
Aslan, Murat Samil
Saranli, Afsar
Baykal, Buyurman
2008 IEEE 16TH SIGNAL PROCESSING, COMMUNICATION AND APPLICATIONS CONFERENCE, VOLS 1 AND 2, 2008, : 729 - +
[23] CLOSED-FORM SOLUTION OF THE CONTINUOUS-TIME LYAPUNOV MATRIX EQUATION
KIM, HC
CHOI, CH
IEE PROCEEDINGS-CONTROL THEORY AND APPLICATIONS, 1994, 141 (05): : 350 - 356
[24] Closed-Form Solutions to Continuous-Time Algebraic Riccati Equation for Second-Order Systems
Rustagi, Vishvendra
Sultan, Cornel
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 2024, 91 (06):
[25] The matrix bounds for the solution matrix of the discrete algebraic riccati equation
Lee, CH
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 1996, 43 (05): : 402 - 407
[26] Matrix Bounds for the Solution of the Continuous Algebraic Riccati Equation
Zhang, Juan
Liu, Jianzhou
MATHEMATICAL PROBLEMS IN ENGINEERING, 2010, 2010
[27] ON THE NUMERICAL-SOLUTION OF THE RICCATI ALGEBRAIC MATRIX EQUATION
ELGINDY, TM
SALIM, MS
FARGHALY, MS
COMMUNICATIONS IN APPLIED NUMERICAL METHODS, 1986, 2 (05): : 483 - 487
[28] DAVIDON METHOD OF SOLUTION OF ALGEBRAIC MATRIX RICCATI EQUATION
MAN, FT
INTERNATIONAL JOURNAL OF CONTROL, 1969, 10 (06) : 713 - +
[29] BOUNDS FOR THE EIGENVALUES OF THE SOLUTION MATRIX OF THE ALGEBRAIC RICCATI EQUATION
YAZ, E
INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, 1985, 16 (07) : 815 - 820
[30] ANALYTIC SOLUTION FOR AN ALGEBRAIC MATRIX RICCATI EQUATION - COMMENT
BIERMAN, GJ
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1975, AC20 (02) : 300 - 301

← 1 2 3 4 5 →