## 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 language | English |
---|---|

Pages (from-to) | 71-97 |

Number of pages | 27 |

Journal | Linear Algebra and Its Applications |

Volume | 683 |

DOIs | |

Publication status | Published - 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