TY - JOUR

T1 - New upper solution bounds of the discrete algebraic Riccati matrix equation

AU - Wiltshire, Ron

AU - Shi, Peng

AU - Davies, Richard

PY - 2007/3/1

Y1 - 2007/3/1

N2 - In this note, we present upper bounds for the solution of the discrete algebraic Riccati equation (DARE). Using the matric 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.

AB - In this note, we present upper bounds for the solution of the discrete algebraic Riccati equation (DARE). Using the matric 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.

KW - matrix bound

KW - discrete algebraic Riccati equation

KW - similarity transformation

U2 - 10.1016/j.cam.2007.01.015

DO - 10.1016/j.cam.2007.01.015

M3 - Article

VL - 213

SP - 307

EP - 315

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

IS - 2

ER -