New upper solution bounds of the discrete algebraic Riccati matrix equation
New upper solution bounds of the discrete algebraic Riccati matrix equation
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DOI：
10.1016/j.cam.2007.01.015
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发表时间：
2008-03
影响因子：
2.4
通讯作者：
Richard Davies;Peng Shi;R. Wiltshire
中科院分区：
文献类型：
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作者：
Richard Davies;Peng Shi;R. Wiltshire
本文给出了离散代数Riccati方程（DARE）解的矩阵上界。然后利用定理2.2的矩阵界，给出了DARE解的几个特征值上界，并与已有结果进行了比较。我们的结果相对于现有上界的优点是，定理2.2和推论2.1的新上界总是在DARE的稳定解存在的情况下计算出来的，而所有现有的矩阵上界都可能不计算，因为它们是在更强的条件下推导出来的。最后，通过数值算例验证了所得结果的有效性。
In this note, we present upper matrix bounds for the solution of the discrete algebraic Riccati equation (DARE). Using the matrix bound of Theorem 2.2, we then give several eigenvalue upper bounds for the solution of the DARE and make comparisons with existing results. The advantage of our results over existing upper bounds is that the new upper bounds of Theorem 2.2 and Corollary 2.1 are always calculated if the stabilizing solution of the DARE exists, whilst all existing upper matrix bounds might not be calculated because they have been derived under stronger conditions. Finally, we give numerical examples to demonstrate the effectiveness of the derived results.