Journal
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
Volume 89, Issue 4, Pages 527-542Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00207160.2011.644276
Keywords
matrix bound; unified coupled algebraic Riccati equation; eigenvalue
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Funding
- National Natural Science Foundation of China [10971176]
- Hunan Provincial Natural Science Foundation of China [10JJ2002]
- Hunan Provincial Innovation Foundation for Postgraduates [CX2011B242]
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In this paper, combining the equivalent form of the unified coupled algebraic Riccati equation (UCARE) with the eigenvalue inequalities of a matrix's sum and product, using the properties of an M-matrix and its inverse matrix, we offer new lower and upper matrix bounds for the solution of the UCARE. Furthermore, applying the derived lower and upper matrix bounds and a fixed-point theorem, an existence uniqueness condition of the solution of the UCARE is proposed. Then, we propose a new fixed-point iterative algorithm for the solution of the UCARE. Finally, we present a corresponding numerical example to demonstrate the effectiveness of our results.
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