A structure-preserving doubling algorithm for continuous-time algebraic Riccati equations

E. K.W. Chu, H. Y. Fan, W. W. Lin

Research output: Contribution to journalArticle

64 Citations (Scopus)

Abstract

Continuous-time algebraic Riccati equations (CAREs) can be transformed, à la Cayley, to discrete-time algebraic Riccati equations (DAREs). The efficient structure-preserving doubling algorithm (SDA) for DAREs, from [E.K.-W. Chu, H.-Y. Fan, W.-W. Lin, A structure-preserving doubling algorithm for periodic discrete-time algebraic Riccati equations, preprint 2002-28, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan, 2003; E.K.-W. Chu, H.-Y. Fan, W.-W. Lin, C.-S. Wang, A structure-preserving doubling algorithm for periodic discrete-time algebraic Riccati equations, preprint 2002-18, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan, 2003], can then be applied. In this paper, we develop the structure-preserving doubling algorithm from a new point of view and show its quadratic convergence under assumptions which are weaker than stabilizability and detectability, as well as practical issues involved in the application of the SDA to CAREs. A modified version of the SDA, developed for DAREs with a "doubly symmetric" structure, is also presented. Extensive numerical results show that our approach is efficient and competitive.

Original languageEnglish
Pages (from-to)55-80
Number of pages26
JournalLinear Algebra and Its Applications
Volume396
Issue number1-3
DOIs
Publication statusPublished - 2005 Feb 1

Keywords

  • Cayley transform
  • Continuous-time algebraic Riccati equation
  • Doubling algorithm
  • Matrix sign function
  • Structure-preserving

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

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