New matrix bounds, an existence uniqueness and a fixed-point iterative algorithm for the solution of the unified coupled algebraic Riccati equation

Abstract

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.

Keywords:

• matrix bound
• unified coupled algebraic Riccati equation
• eigenvalue

2010 AMS Subject Classifications :

• 15A18
• 15A24
• 15A42
• 93B05

Acknowledgements

The author would like to thank Professor Choi-Hong Lai and the referees for their very helpful comments and suggestions. The work was supported in part by the National Natural Science Foundation of China (10971176), the Key Project of Hunan Provincial Natural Science Foundation of China (10JJ2002) and the Hunan Provincial Innovation Foundation for Postgraduates (CX2011B242).