New matrix bounds and iterative algorithms for the discrete coupled algebraic Riccati equation |
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| Authors: | Jianzhou Liu Li Wang Juan Zhang |
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| Affiliation: | 1. Department of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, P. R. China;2. College of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, Hunan, P. R. China;3. College of Science, National University of Defense Technology, Changsha, Hunan, P. R. China |
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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. |
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| Keywords: | Matrix bound discrete algebraic Riccati equation eigenvalue |
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