New upper solution bounds of the discrete algebraic Riccati matrix equation

Authors:
Richard Davies;Peng Shi;Ron Wiltshire
Affiliations:
Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL, UK;Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL, UK;Faculty of Advanced Technology, University of Glamorgan, Pontypridd CF37 1DL, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 2
Cited 1

Discrete-time control systems (2nd ed.)

Discrete-time control systems (2nd ed.)
Solution bounds for the discrete Riccati equation and its applications

Journal of Optimization Theory and Applications

Brief paper: Upper solution bounds of the continuous and discrete coupled algebraic Riccati equations

Automatica (Journal of IFAC)

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Abstract

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.