New upper solution bounds of the discrete algebraic Riccati matrix equation

Ron Wiltshire, Peng Shi, Richard Davies

Research output: Contribution to journalArticlepeer-review

Abstract

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.
Original languageEnglish
Pages (from-to)307 - 315
Number of pages8
JournalJournal of Computational and Applied Mathematics
Volume213
Issue number2
DOIs
Publication statusPublished - 1 Mar 2007

Keywords

  • matrix bound
  • discrete algebraic Riccati equation
  • similarity transformation

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