The Analytic Solutions of the Homogeneous Modified Algebraic Riccati Equation

Liangyin Zhang; Michael Z. Q. Chen; Chanying Li

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The Analytic Solutions of the Homogeneous Modified Algebraic Riccati Equation

机译：齐次代数Riccati方程的解析解。

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摘要

In this note, a discrete-time modified algebraic Riccati equation (MARE) is investigated. First, the analytic solutions of the homogeneous MARE for controllable single-input systems are explicitly obtained in terms of the system eigenvalues. For anti-Schur systems, the stabilizing, and positive definite solution is proposed. Furthermore, the maximal solution and the solution bound are analyzed for the nonhomogeneous MARE.

机译：在本文中，研究了离散时间修正的代数Riccati方程（MARE）。首先，根据系统特征值明确获得可控制单输入系统的齐次MARE的解析解。对于反舒尔系统，提出了稳定的正定解。此外，分析了非均匀MARE的最大解和解界。

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来源
《IEEE Transactions on Automatic Control》 |2017年第9期|4834-4839|共6页
作者
Liangyin Zhang; Michael Z. Q. Chen; Chanying Li;
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作者单位

School of Automation, Nanjing University of Science and Technology, Nanjing, China;

School of Automation, Nanjing University of Science and Technology, Nanjing, China;

Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China;

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正文语种 eng
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关键词
Eigenvalues and eigenfunctions; Partitioning algorithms; Riccati equations; Optimal control; Electronic mail; Symmetric matrices;

机译：特征值和特征函数;划分算法;Riccati方程;最优控制;电子邮件;对称矩阵;

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专利

1. On the Existence of a Stabilizing Solution of Modified Algebraic Riccati Equations in Terms of Standard Algebraic Riccati Equations and Linear Matrix Inequalities [J] . Francisco J. Vargas, Rodrigo A. González IEEE Control Systems Letters . 2020,第1期

机译：关于标准代数Riccati方程和线性矩阵不等式的修正代数Riccati方程的稳定解的存在性
2. Homotopy methods for the solution of general modified algebraic Riccati equations [J] . Richter S., Hodel A.S. IEE Proceedings. Part D . 1993,第6期

机译：一般修正代数Riccati方程解的同伦方法
3. The dual algebraic Riccati equations and the set of all solutions of the discrete-time Riccati equation [J] . Zhang Liangyin, Chen Michael Z. Q., Li Chanying International Journal of Control . 2017,第7a9期

机译：双代数Riccati方程和离散时间Riccati方程的所有解决方案集
4. Homotopy methods for the solution of general modified algebraic Riccati equations [C] . Richter, S., Hodel, . 1990

机译：一般修正代数Riccati方程解的同伦方法
5. Numerical solution of the coupled algebraic riccati equations. [D] . Rajasingam, Prasanthan. 2013

机译：耦合代数riccati方程的数值解。
6. RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations [O] . Peter Benner, Zvonimir Bujanović, Patrick Kürschner, -1

机译：RADI：低阶ADI型算法用于大规模代数Riccati方程
7. The solution set of the algebraic Riccati equation and the algebraic Riccati inequality [O] . Scherer Carsten 1991

机译：代数Riccati方程的解集和代数Riccati不等式

The Analytic Solutions of the Homogeneous Modified Algebraic Riccati Equation

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