Inheritance properties of the conjugate discrete-time algebraic Riccati equation

Chun Yueh Chiang, Hung Yuan Fan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under mild and reasonable assumptions, the existence of the maximal solution to the conjugate discrete-time Riccati equation, in which the control weighting matrix is nonsingular and its constant term is Hermitian, will be inherited to a transformed discrete-time algebraic Riccati equation. Based on this inheritance property, an accelerated fixed-point iteration is proposed for finding the maximal solution via the transformed Riccati equation. Numerical examples are shown to illustrate the correctness of our theoretical results and the feasibility of the proposed algorithm.

Original languageEnglish
Pages (from-to)71-97
Number of pages27
JournalLinear Algebra and Its Applications
Volume683
DOIs
Publication statusPublished - 2024 Feb 15

Keywords

  • Antilinear system
  • Conjugate discrete-time algebraic Riccati equation
  • Fixed-point iteration
  • Inheritance property
  • LQR control problem
  • Maximal solution

ASJC Scopus subject areas

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

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