An iterative algorithm for the solution of the discrete-time algebraic Riccati equation

Lin Zhang Lu*, Wen-Wei Lin

*Corresponding author for this work

Research output: Contribution to journalArticle

19 Scopus citations

Abstract

The discrete-time algebraic Riccati equation is solved in this study by an iterative algorithm for the square root of a squared Hamiltonian matrix, which is obtained from the S + -1 transformation of the symplectic pencil associated with the Riccati equation. The symplectic Givens and n × n block-diagonal orthogonal transformations are used before the iterative process so that the iteration is structure-preserving and can achieve on average 60% reduction of computation time compared with the QZ algorithm. A formal analysis for roundoff errors and some numerical examples are also given.

Original languageEnglish
Pages (from-to)465-488
Number of pages24
JournalLinear Algebra and Its Applications
Volume188-189
Issue numberC
DOIs
StatePublished - 1 Jan 1993

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