Comments on "An Inversion-Free Iterative Algorithm for Riccati Matrix Equations in Discrete-Time Markov Jump Systems"

Discrete coupled Riccati matrix equations, which play an important role in the analysis and design of discrete-time Markov jump systems of control theory, have been studied extensively. In Li et al. (2022), an iterative algorithm for positive definite solutions of these matrix equations was presented. This article gives numerical examples to point out that the convergence proof of the iterative algorithm proposed in the above paper cites an incorrect conclusion, resulting in errors in the convergence proof of the iterative algorithm as well as the entire algorithm.