The existence uniqueness and the fixed iterative algorithm of the solution for the discrete coupled algebraic Riccati equation |
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| Authors: | Jianzhou Liu Juan Zhang |
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| Affiliation: | 1. Department of Mathematics and Computational Science , Xiangtan University , Xiangtan, Hunan 411105, P.R. China liujz@xtu.edu.cn;3. Department of Mathematics and Computational Science , Xiangtan University , Xiangtan, Hunan 411105, P.R. China |
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| Abstract: | In this article, applying the properties of M-matrix and non-negative matrix, utilising eigenvalue inequalities of matrix's sum and product, we firstly develop new upper and lower matrix bounds of the solution for discrete coupled algebraic Riccati equation (DCARE). Secondly, we discuss the solution existence uniqueness condition of the DCARE using the developed upper and lower matrix bounds and a fixed point theorem. Thirdly, a new fixed iterative algorithm of the solution for the DCARE is shown. Finally, the corresponding numerical examples are given to illustrate the effectiveness of the developed results. |
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| Keywords: | matrix bound discrete algebraic Riccati equation eigenvalue |
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