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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Vydáno v:International journal of control Ročník 90; číslo 11; s. 2326 - 2337
Hlavní autoři: Liu, Jianzhou, Wang, Li, Zhang, Juan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 02.11.2017
Taylor & Francis Ltd
Témata:
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
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Abstract 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.
AbstractList 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.
Author Liu, Jianzhou
Zhang, Juan
Wang, Li
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SubjectTerms Algebra
Algorithms
Control theory
discrete algebraic Riccati equation
eigenvalue
Inequalities
Iterative algorithms
Iterative methods
Matrix bound
Nonlinear programming
Riccati equation
Title New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation
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