A latest update-based inversion-free iterative algorithm for solving discrete periodic Riccati equations

This paper focuses on solving discrete periodic Riccati matrix equations (DPREs) that arise in the optimal control of discrete-time periodic linear systems. Based on the Schulz iteration, an equivalent reformulation without matrix inversion is constructed. With the help of it, a novel inversion-free iterative algorithm is presented by introducing a tuning parameter and the latest estimation. Moreover, the R-convergence factor of the resulting iterative sequences is rigorously derived to quantitatively characterize the convergence rate. Additional convergence properties of the proposed algorithm are also analyzed in detail. Finally, numerical simulations show that the proposed method outperforms existing approaches in both convergence rate and computational efficiency, indicating its superiority in solving DPREs arising from large-scale systems.