UNMIXED SOLUTIONS OF THE DISCRETE-TIME ALGEBRAIC RICCATI EQUATION

被引：12

作者：

WIMMER, HK

机构：

[1] Universitat Wurzburg, Wurzburg

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 1992年 / 30卷 / 04期

关键词：

DISCRETE-TIME ALGEBRAIC RICCATI EQUATION; SYMPLECTIC PENCILS; UNMIXED SOLUTIONS; MODULUS CONTROLLABILITY; MAXIMAL SOLUTION;

D O I：

10.1137/0330048

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 algebraic Riccati equation of the optimal control problem associated with the discrete-time system x(k + 1) = Fx(k) + Gu(k) is studied. It is shown that in the case of a controllable system, there exist solutions with prescribed unmixed characteristic polynomial of the corresponding closed-loop matrix. Existence of solutions will also be proved under the weaker condition of modulus-controllability. Maximal solutions are discussed.

引用

页码：867 / 878

页数：12

共 32 条

[1] Existence and uniqueness of unmixed solutions of the discrete-time algebraic Riccati equation
Clements, DJ
Wimmer, HK
SYSTEMS & CONTROL LETTERS, 2003, 50 (05) : 343 - 346
[2] A parametrization of solutions of the discrete-time algebraic Riccati equation based on pairs of opposite unmixed solutions
Wimmer, HK
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2006, 44 (06) : 1992 - 2005
[3] Existence of unmixed solutions of the discrete-time algebraic Riccati equation and a nonstrictly bounded real lemma
Wimmer, HK
SYSTEMS & CONTROL LETTERS, 2001, 43 (02) : 141 - 147
[4] Intervals of solutions of the discrete-time algebraic Riccati equation
Wimmer, HK
SYSTEMS & CONTROL LETTERS, 1999, 36 (03) : 207 - 212
[5] A characterization of solutions of the discrete-time algebraic Riccati equation based on quadratic difference forms
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Takaba, Kiyotsugu
Kaneko, Osamu
Rapisarda, Paolo
LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 416 (2-3) : 1060 - 1082
[6] On the maximal solution of the conjugate discrete-time algebraic Riccati equation
Fan, Hung-Yuan
Chiang, Chun-Yueh
APPLIED MATHEMATICS LETTERS, 2023, 135
[7] Inheritance properties of the conjugate discrete-time algebraic Riccati equation
Chiang, Chun-Yueh
Fan, Hung-Yuan
LINEAR ALGEBRA AND ITS APPLICATIONS, 2024, 683 : 71 - 97
[8] On the structure of the solutions of discrete-time algebraic Riccati equation with singular closed-loop matrix
Ferrante, A
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2004, 49 (11) : 2049 - 2054
[9] The Estimation of the Solutions Matrix of the Perturbed Discrete Time Algebraic Riccati Equation
Bi, Hai-yun
Chen, Dong-yan
PROCEEDINGS OF THE 10TH WORLD CONGRESS ON INTELLIGENT CONTROL AND AUTOMATION (WCICA 2012), 2012, : 1172 - 1175
[10] Robust verification algorithm for stabilizing solutions of discrete-time algebraic Riccati equations
Shinya Miyajima
Japan Journal of Industrial and Applied Mathematics, 2019, 36 : 763 - 776

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