TY - JOUR

T1 - On the maximal solution of the conjugate discrete-time algebraic Riccati equation

AU - Fan, Hung Yuan

AU - Chiang, Chun Yueh

N1 - Funding Information:
This research work is partially supported by the National Science and Technology Council of Taiwan and the National Center for Theoretical Sciences of Taiwan. The first author (Hung-Yuan Fan) would like to thank the support from the National Science and Technology Council of Taiwan under the grant MOST 110-2115-M-003-016 , and the corresponding author (Chun-Yueh Chiang) would like to thank the support from the National Science and Technology Council of Taiwan under the grant MOST 109-2115-M-150-003-MY2 .
Publisher Copyright:
© 2022 Elsevier Ltd

PY - 2023/1

Y1 - 2023/1

N2 - 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 some mild assumptions and the framework of the fixed-point iteration, a constructive proof is given for 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. Moreover, starting with a suitable initial matrix, we also show that the nonincreasing sequence generated by the fixed-point iteration converges at least linearly to the maximal solution of the Riccati equation. An example is given to demonstrate the correctness of our main theorem and provide considerable insights into the study of another meaningful solutions.

AB - 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 some mild assumptions and the framework of the fixed-point iteration, a constructive proof is given for 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. Moreover, starting with a suitable initial matrix, we also show that the nonincreasing sequence generated by the fixed-point iteration converges at least linearly to the maximal solution of the Riccati equation. An example is given to demonstrate the correctness of our main theorem and provide considerable insights into the study of another meaningful solutions.

KW - Antilinear system

KW - Conjugate discrete-time algebraic Riccati equation

KW - Conjugate Stein matrix equation

KW - Fixed-point iteration

KW - LQR control problem

KW - Maximal solution

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U2 - 10.1016/j.aml.2022.108438

DO - 10.1016/j.aml.2022.108438

M3 - Article

AN - SCOPUS:85138418748

VL - 135

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

M1 - 108438

ER -