New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation

The discrete coupled algebraic Riccati equation (DCARE) has wide applications in control theory and linear system. In general, for the DCARE, one discusses every term of the coupled term, respectively. In this paper, we consider the coupled term as a whole, which is different from the recent results...

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Bibliographic Details
Published in:International journal of control Vol. 90; no. 11; pp. 2326 - 2337
Main Authors: Liu, Jianzhou, Wang, Li, Zhang, Juan
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 02.11.2017
Taylor & Francis Ltd
Subjects:
Algebra
Algorithms
Control theory
discrete algebraic Riccati equation
eigenvalue
Inequalities
Iterative algorithms
Iterative methods
Matrix bound
Nonlinear programming
Riccati equation
ISSN:0020-7179, 1366-5820
Online Access:Get full text
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Summary:The discrete coupled algebraic Riccati equation (DCARE) has wide applications in control theory and linear system. In general, for the DCARE, one discusses every term of the coupled term, respectively. In this paper, we consider the coupled term as a whole, which is different from the recent results. When applying eigenvalue inequalities to discuss the coupled term, our method has less error. In terms of the properties of special matrices and eigenvalue inequalities, we propose several upper and lower matrix bounds for the solution of DCARE. Further, we discuss the iterative algorithms for the solution of the DCARE. In the fixed point iterative algorithms, the scope of Lipschitz factor is wider than the recent results. Finally, we offer corresponding numerical examples to illustrate the effectiveness of the derived results.
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ISSN:0020-7179
1366-5820
DOI:10.1080/00207179.2016.1245867