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.

翻译：在本文中,我们考虑的是一类离散的离散时间里卡蒂方程式,最初产生于离散的反线性系统线性二次调控问题,根据一些温和假设和固定点迭代框架,对共聚离时间里卡蒂方程式存在最大解决办法提供了建设性证据,在这种公式中,控制加权矩阵是非同质的,其持续期限是Hermitian。此外,从适当的初始矩阵开始,我们还表明固定点迭代产生的非递增序列至少线性地汇合到里卡蒂方程式的最大解决方案,举例表明我们主要理论的正确性,并为研究其他有意义的解决方案提供大量见解。