  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.
